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Автор: Grafiati

Опубліковано: 26 жовтня 2023

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1

Agrawal, Purshottam, Dharmendra Kumar, and Behar Baxhaku. "On the rate of convergence of modified \(\alpha\)-Bernstein operators based on q-integers." Journal of Numerical Analysis and Approximation Theory 51, no. 1 (September 17, 2022): 3–36. http://dx.doi.org/10.33993/jnaat511-1244.

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Анотація:

In the present paper we define a q-analogue of the modified a-Bernstein operators introduced by Kajla and Acar (Ann. Funct. Anal. 10 (4) 2019, 570-582). We study uniform convergence theorem and the Voronovskaja type asymptotic theorem. We determine the estimate of error in the approximation by these operators by virtue of second order modulus of continuity via the approach of Steklov means and the technique of Peetre's \(K\)-functional. Next, we investigate the Gruss- Voronovskaya type theorem. Further, we define a bivariate tensor product of these operatos and derive the convergence estimates by utilizing the partial and total moduli of continuity. The approximation degree by means of Peetre's K- functional , the Voronovskaja and Gruss Voronovskaja type theorems are also investigated. Lastly, we construct the associated GBS (Generalized Boolean Sum) operator and examine its convergence behavior by virtue of the mixed modulus of smoothness.

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2

Kajla, Arun, S. A. Mohiuddine та Abdullah Alotaibi. "Approximation by α-Baskakov−Jain type operators". Filomat 36, № 5 (2022): 1733–41. http://dx.doi.org/10.2298/fil2205733k.

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Анотація:

In this manuscript, we consider the Baskakov-Jain type operators involving two parameters ? and ?. Some approximation results concerning the weighted approximation are discussed. Also, we find a quantitative Voronovskaja type asymptotic theorem and Gr?ss Voronovskaya type approximation theorem for these operators. Some numerical examples to illustrate the approximation of these operators to certain functions are also given.

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3

Acar, Tuncer. "Quantitative q-Voronovskaya and q-Grüss–Voronovskaya-type results for q-Szász operators." Georgian Mathematical Journal 23, no. 4 (December 1, 2016): 459–68. http://dx.doi.org/10.1515/gmj-2016-0007.

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Анотація:

AbstractIn the present paper, we mainly study quantitative Voronovskaya-type theorems for q-Szász operators defined in [20]. We consider weighted spaces of functions and the corresponding weighted modulus of continuity. We obtain the quantitative q-Voronovskaya-type theorem and the q-Grüss–Voronovskaya-type theorem in terms of the weighted modulus of continuity of q-derivatives of the approximated function. In this way, we either obtain the rate of pointwise convergence of q-Szász operators or we present these results for a subspace of continuous functions, although the classical ones are valid for differentiable functions.

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4

Galt, S. G. "VORONOVSKAYA-TYPE THEOREM FOR POSITIVE LINEAR OPERATORS BASED ON LAGRANGE INTERPOLATION." Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application 15, no. 1-2 (2023): 86–93. http://dx.doi.org/10.56082/annalsarscimath.2023.1-2.86.

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Анотація:

Since the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange-Hermite interpolation formula, in the recent paper Gal [3], I have obtained semi-discrete quantitative Voronovskaya-type theorems based on other Lagrange-Hermite interpolation formulas, like Lagrange interpolation on two and three simple knots and Hermite interpolation on two knots, one simple and the other one double. In the present paper we obtain a semi-discrete quantitative Voronovskaya-type theorem based on Lagrange interpolation on arbitrary p + 1 simple distinct knots.

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5

Ivan, Mircea, and Ioan Raşa. "A Voronovskaya-type theorem." Journal of Numerical Analysis and Approximation Theory 30, no. 1 (February 1, 2001): 47–54. http://dx.doi.org/10.33993/jnaat301-680.

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6

Braha, Naim Latif, Toufik Mansour, and Mohammad Mursaleen. "Some Properties of Kantorovich-Stancu-Type Generalization of Szász Operators including Brenke-Type Polynomials via Power Series Summability Method." Journal of Function Spaces 2020 (August 14, 2020): 1–15. http://dx.doi.org/10.1155/2020/3480607.

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Анотація:

In this paper, we study the Kantorovich-Stancu-type generalization of Szász-Mirakyan operators including Brenke-type polynomials and prove a Korovkin-type theorem via the T-statistical convergence and power series summability method. Moreover, we determine the rate of the convergence. Furthermore, we establish the Voronovskaya- and Grüss-Voronovskaya-type theorems for T-statistical convergence.

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7

Braha, Naim L. "Some properties of modified Szász–Mirakyan operators in polynomial spaces via the power summability method." Journal of Applied Analysis 26, no. 1 (June 1, 2020): 79–90. http://dx.doi.org/10.1515/jaa-2020-2006.

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Анотація:

AbstractIn this paper we will prove the Korovkin type theorem for modified Szász–Mirakyan operators via A-statistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods, and in the last section, we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss–Voronovskaya type theorem.

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8

Grewal, Brijesh, and Meenu Goyal. "Approximation by a family of summation-integral type operators preserving linear functions." Filomat 36, no. 16 (2022): 5563–72. http://dx.doi.org/10.2298/fil2216563g.

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Анотація:

This article investigates the approximation properties of a general family of positive linear operators defined on the unbounded interval [0,?). We prove uniform convergence theorem and Voronovskayatype theorem for functions with polynomial growth. More precisely, we study weighted approximation i.e basic convergence theorems, quantitative Voronovskaya-asymptotic theorems and Gr?ss Voronovskayatype theorems in weighted spaces. Finally, we obtain the rate of convergence of these operators via a suitable weighted modulus of continuity.

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9

Uysal, Gümrah. "ON MODIFIED MOMENT-TYPE OPERATORS." Advances in Mathematics: Scientific Journal 10, no. 12 (December 18, 2021): 3669–77. http://dx.doi.org/10.37418/amsj.10.12.9.

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Анотація:

We propose a modification for moment-type operators in order to preserve the exponential function $e^{2cx}$ with $c>0$ on real axis. First, we present moment identities. Then, we prove two weighted convergence theorems. Finally, we present a Voronovskaya-type theorem for the new operators.

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10

Gupta, Vijay, and P. N. Agrawal. "Approximation by modified Păltănea operators." Publications de l'Institut Math?matique (Belgrade) 107, no. 121 (2020): 157–64. http://dx.doi.org/10.2298/pim2021157g.

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Анотація:

We discuss some approximation properties of hybrid genuine operators. We find central moments using the concept of moment generating function. A quantitative Voronovskaya and Gruss-Voronovskaya type theorem are proven. Also, we obtain the degree of approximation of the considered operators by means of the second order Ditzian-Totik modulus of smoothness.

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11

Marsden, M. J. "A Voronovskaya Theorem for Variation-Diminishing Spline Approximation." Canadian Journal of Mathematics 38, no. 5 (October 1, 1986): 1081–93. http://dx.doi.org/10.4153/cjm-1986-053-0.

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Анотація:

In [7] Schoenberg introduced the following variation-diminishing spline approximation methods.Let m > 1 be an integer and let Δ = {xi} be a biinfinite sequence of real numbers with xi ≧ xi + l < xi+m. To a function f associate the spline function Vf of order m with knots Δ defined by(1.1)whereand the Nj(x) are B-splines with support xj < x < xj+m normalized so that ΣjNj(x) = 1. See, e.g., [2] for a precise definition of the Nj(x) and a discussion of the properties of Vf.

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12

Ciupa, Alexandra. "A Voronovskaya-type theorem for a positive linear operator." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–7. http://dx.doi.org/10.1155/ijmms/2006/42368.

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13

Tunç, Tuncay, and Burcu Fedakar. "On Approximation Properties of a Stancu Generalization of Szasz-Mirakyan-Bernstein Operators." Ukrainian Mathematical Bulletin 18, no. 4 (November 12, 2021): 569–82. http://dx.doi.org/10.37069/1810-3200-2021-18-4-8.

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Анотація:

In this paper, we have introduced a Stancu generalization of the Szasz-Mirakyan-Bernstein Operators defined on the space of continuous functions defined on a compact interval. We have given a general formula for the moments of that operators. We have used Korovkin's Theorem for uniform approximation under some restrictions. We have obtained some results for the approximation rates in terms of modulus of continuity. Finally, we gave some Voronovskaya-type theorems.

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14

Liu, Yu-Jie, Wen-Tao Cheng, Wen-Hui Zhang, and Pei-Xin Ye. "Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators." Axioms 12, no. 1 (December 21, 2022): 5. http://dx.doi.org/10.3390/axioms12010005.

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Анотація:

We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive the Voronovskaya-type asymptotic theorem for this type of operator. Then, the local and global approximation theorems are obtained by using the classical modulus of continuity and K-functional. Finally, we derive the rate of convergence for functions with a derivative of bounded variation. The results show that the new operators have good approximation properties.

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15

Başcanbaz-Tunca, Gülen, and Ayçegül Erençin. "A Voronovskaya type theorem for q-Szász-Mirakyan-Kantorovich operators." Journal of Numerical Analysis and Approximation Theory 40, no. 1 (February 1, 2011): 14–23. http://dx.doi.org/10.33993/jnaat401-947.

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Анотація:

In this work, we consider a Kantorovich type generalization of \(q\)-Szász-Mirakyan operators via Riemann type \(q\)-integral and prove a Voronovskaya type theorem by using suitable machinery of \(q\)-calculus.

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16

Mishra, Vishnu Narayan, and Rishikesh Yadav. "Approximation on a new class of Szász–Mirakjan operators and their extensions in Kantorovich and Durrmeyer variants with applicable properties." Georgian Mathematical Journal 29, no. 2 (January 28, 2022): 245–73. http://dx.doi.org/10.1515/gmj-2021-2135.

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Анотація:

Abstract This paper deals with the approximation properties of a generalized version of Szász–Mirakjan operators which preserve a x {a^{x}} , a > 1 {a>1} (fixed), and x ≥ 0 {x\geq 0} . The uniform convergence of the operators is studied by using some auxiliary results. Also, error estimations are determined by considering the functions from different spaces. The convergence of the said operators is shown and analyzed by graphics. In the same direction, the proposed operators are compared with Szász–Mirakjan operators for the rate of convergence. A Voronovskaya-type theorem is considered and a comparison with Szász–Mirakjan operators is shown in the sense of convexity. To describe the quantitative means of an asymptotic formula, we quantitatively approach the Voronovskaya-type theorem; moreover, a Grüss–Voronovskaya-type theorem is proved. For further investigations regarding the approximation for functions from various spaces, two significant extensions are added keeping in mind some developments in the L p {L_{p}} -space. One is the Kantorovich variant and the other one is the Durrmeyer modification of the defined operators. Here, the rate of convergence is described by means of the function with a derivative of bounded variation for the Durrmeyer modified operators for which some properties are discussed. Also, A-statistical properties of the Durrmeyer modified operators are established. This paper ends by presenting some significant statements and the conclusion.

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17

ARI, DIDEM AYDIN, ALI ARAL та DANIEL CARDENAS-MORALES. "A note on Baskakov operators based on a function ϑ". Creative Mathematics and Informatics 25, № 1 (2016): 15–27. http://dx.doi.org/10.37193/cmi.2016.01.03.

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Анотація:

In this paper, we consider a modification of the classical Baskakov operators based on a function ϑ. Basic qualitative and quantitative Korovkin results are stated in weighted spaces. We prove a quantitative Voronovskaya-type theorem and present some results on the monotonic convergence of the sequence. Finally, we show a shape preserving property and further direct convergence theorems. Weighted modulus of continuity of first order and the notion of ϑ-convexity are used throughout the paper

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18

Aslan, Reşat, and Aydın İzgi. "Approximation by One and Two Variables of the Bernstein-Schurer-Type Operators and Associated GBS Operators on Symmetrical Mobile Interval." Journal of Function Spaces 2021 (May 3, 2021): 1–12. http://dx.doi.org/10.1155/2021/9979286.

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Анотація:

In this article, we purpose to study some approximation properties of the one and two variables of the Bernstein-Schurer-type operators and associated GBS (Generalized Boolean Sum) operators on a symmetrical mobile interval. Firstly, we define the univariate Bernstein-Schurer-type operators and obtain some preliminary results such as moments, central moments, in connection with a modulus of continuity, the degree of convergence, and Korovkin-type approximation theorem. Also, we derive the Voronovskaya-type asymptotic theorem. Further, we construct the bivariate of this newly defined operator, discuss the order of convergence with regard to Peetre’s K -functional, and obtain the Voronovskaya-type asymptotic theorem. In addition, we consider the associated GBS-type operators and estimate the order of approximation with the aid of mixed modulus of smoothness. Finally, with the help of the Maple software, we present the comparisons of the convergence of the bivariate Bernstein-Schurer-type and associated GBS operators to certain functions with some graphical illustrations and error estimation tables.

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19

Rempulska, Lucyna, and Mariola Skorupka. "On the degree of approximation of functions of two variables by some operators." Acta et Commentationes Universitatis Tartuensis de Mathematica 9 (December 31, 2005): 51–64. http://dx.doi.org/10.12697/acutm.2005.09.07.

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Анотація:

We introduce operators of Szász-Mirakyan and Baskakov type in polynomial weighted spaces of functions of two variables. We prove a theorem on the degree of approximation and a Voronovskaya type theorem for these operators. Similar results for Bernstein, Szász-Mirakyan and Baskakov operators of functions of one variable were given in [3-6].

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20

Braha, Naim L., and Valdete Loku. "Statistical Korovkin and Voronovskaya type theorem for the Cesaro second-order operator of fuzzy numbers." Studia Universitatis Babes-Bolyai Matematica 65, no. 4 (November 26, 2020): 561–74. http://dx.doi.org/10.24193/subbmath.2020.4.06.

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Анотація:

In this paper we define the Ces\'aro second-order summability method for fuzzy numbers and prove Korovkin type theorem, then as the application of it, we prove the rate of convergence. In the last section, we prove the kind of Voronovskaya type theorem and give some concluding remarks related to the obtained results.

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21

Lampa-Baczynska, Magdalena. "A Voronovskaya Type Theorem for Bernstein-Durrmeyer Type Operators." British Journal of Mathematics & Computer Science 10, no. 3 (January 10, 2015): 1–6. http://dx.doi.org/10.9734/bjmcs/2015/18471.

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22

Mohiuddine, S. A., Bipan Hazarika, and Mohammed Alghamdi. "Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems." Filomat 33, no. 14 (2019): 4549–60. http://dx.doi.org/10.2298/fil1914549m.

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Анотація:

We introduce the notion of ideally relative uniform convergence of sequences of real valued functions. We then apply this notion to prove Korovkin-type approximation theorem, and then construct an illustrative example by taking (p,q)-Bernstein operators which proves that our Korovkin theorem is stronger than its classical version as well as statistical relative uniform convergence. The rate of ideal relatively uniform convergence of positive linear operators by means of modulus of continuity is calculated. Finally, the Voronovskaya-type approximation theorem is also investigated.

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23

Erdogan, S., and A. Olgun. "Approximation properties of modified Jain-Gamma operators." Carpathian Mathematical Publications 13, no. 3 (December 7, 2021): 651–65. http://dx.doi.org/10.15330/cmp.13.3.651-665.

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Анотація:

In the present paper, we study some approximation properties of a modified Jain-Gamma operator. Using Korovkin type theorem, we first give approximation properties of such operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we present approximation properties of weighted spaces. Finally, we obtain the Voronovskaya type theorem of this operator.

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24

Hussein, Sara Adel. "Approximation by General Family of Summation Baskakov-Type Operators Preserving the Exponential Functions." BASRA JOURNAL OF SCIENCE 39, no. 3 (December 1, 2021): 329–38. http://dx.doi.org/10.29072/basjs.2021301.

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Анотація:

The present paper is defining and studding a modification of the general family sequence of summation Baskakov-type operators. This modification is preserved that the functions and where is fixed. We show that the uniform convergence theorem of this sequence by using the modulus of continuity to the function being approximated. Finally, we introduce the asymptotic formula for the Voronovskaya-type theorem

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25

Qasim, Mohd, M. Mursaleen, Zaheer Abbas, and Asif Khan. "Approximation by generalized Szász-Mirakjan-Kantorovich type operators." Publications de l'Institut Math?matique (Belgrade) 111, no. 125 (2022): 89–99. http://dx.doi.org/10.2298/pim2225089q.

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Анотація:

We construct Kantorovich variant of generalized Sz?sz-Mirakjan operators whose construction depends on a continuously differentiable, increasing and unbounded function ?. For these new operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.

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26

Neer, Trapti, and P. N. Agrawal. "A genuine family of Bernstein-Durrmeyer type operators based on Polya basis functions." Filomat 31, no. 9 (2017): 2611–23. http://dx.doi.org/10.2298/fil1709611n.

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Анотація:

In this paper, we construct a genuine family of Bernstein-Durrmeyer type operators based on Polya basis functions. We establish some moment estimates and the direct results which include global approximation theorem in terms of classical modulus of continuity, local approximation theorem in terms of the second order Ditizian-Totik modulus of smoothness, Voronovskaya-type asymptotic theorem and a quantitative estimate of the same type. Lastly, we study the approximation of functions having a derivative of bounded variation.

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27

Qasim, M., A. Khan, Z. Abbas, and M. Mursaleen. "Convergence properties of generalized Lupaş-Kantorovich operators." Carpathian Mathematical Publications 13, no. 3 (December 30, 2021): 818–30. http://dx.doi.org/10.15330/cmp.13.3.818-830.

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Анотація:

In the present paper, we consider the Kantorovich modification of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing and unbounded function $\rho$. For these new operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.

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28

Aktaş, Rabia, Bayram Çekim, and Fatma Taşdelen. "A Kantorovich-Stancu Type Generalization of Szasz Operators including Brenke Type Polynomials." Journal of Function Spaces and Applications 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/935430.

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Анотація:

We introduce a Kantorovich-Stancu type modification of a generalization of Szasz operators defined by means of the Brenke type polynomials and obtain approximation properties of these operators. Also, we give a Voronovskaya type theorem for Kantorovich-Stancu type operators including Gould-Hopper polynomials.

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29

Anastassiou, George A., and Razvan A. Mezei. "A Voronovskaya Type Theorem for Poisson–Cauchy Type singular operators." Journal of Mathematical Analysis and Applications 366, no. 2 (June 2010): 525–29. http://dx.doi.org/10.1016/j.jmaa.2010.01.015.

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30

JIANG, YANJIE, and JUNMING LI. "THE RATE OF CONVERGENCE OF q-BERNSTEIN–STANCU POLYNOMIALS." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 06 (November 2009): 773–79. http://dx.doi.org/10.1142/s0219691309003215.

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Анотація:

Let q > 0, α ≥ 0, f ∈ C[0, 1], and [Formula: see text] be the q-Bernstein–Stancu polynomials. In the case α = 0, [Formula: see text] reduces to the well-known q-Bernstein polynomials introduced by Phillips in 1997. In this paper, we study the rate of convergence of the sequence [Formula: see text]. Both a theorem on convergence and a Voronovskaya-type theorem on the rate of convergence are proved.

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31

Aral, Ali, Emre Deniz, and Vijay Gupta. "On the modification of the Szaśz–Durrmeyer operators." Georgian Mathematical Journal 23, no. 3 (September 1, 2016): 323–28. http://dx.doi.org/10.1515/gmj-2016-0031.

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Анотація:

AbstractIn this paper we consider the modification of Szász–Durrmeyer operators based on the Jain basis function. Voronovskaya-type estimates of point-wise convergence along with its quantitative version based on the weighted modulus of smoothness are given. Moreover, a direct approximation theorem for the operators is proved.

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32

Rao, Nadeem, and Abdul Wafi. "Stancu-variant of generalized Baskakov operators." Filomat 31, no. 9 (2017): 2625–32. http://dx.doi.org/10.2298/fil1709625r.

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Анотація:

In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.

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33

QASIM, MOHD, M. MURSALEEN, ASIF KHAN, and ZAHEER ABBAS. "On some Statistical Approximation Properties of Generalized Lupas-Stancu Operators." Kragujevac Journal of Mathematics 46, no. 5 (2022): 797–813. http://dx.doi.org/10.46793/kgjmat2205.797q.

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Анотація:

The purpose of this paper is to introduce Stancu variant of generalized Lupaş operators whose construction depends on a continuously diﬀerentiable, increasing and unbounded function ρ. Depending on the selection of γ and δ, these operators are more ﬂexible than the generalized Lupaş operators while retaining their approximation properties. For these operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.

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34

Icoz, Gurhan, and Seda Demir. "Approximation Properties of a New Type of Gamma Operator Defined with the Help of k -Gamma Function." Journal of Function Spaces 2022 (August 2, 2022): 1–9. http://dx.doi.org/10.1155/2022/5493056.

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Анотація:

With the help of the k -Gamma function, a new form of Gamma operator is given in this article. Voronovskaya type theorem, weighted approximation, rates of convergence, and pointwise estimates have been found for approximation features of the newly described operator. Finally, numerical examples have been provided to demonstrate that the operator is approaching the function.

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35

Agrawal, Deepika, and Vijay Gupta. "Generalized hybrid operators preserving exponential functions." Asian-European Journal of Mathematics 12, no. 07 (November 18, 2019): 1950089. http://dx.doi.org/10.1142/s179355711950089x.

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Анотація:

The present paper deals with the approximation properties of generalization of Lupaş–Păltănea’s operators preserving exponential functions. We obtain moments using the concept of moment generating functions and establish a Voronovskaya type theorem, uniform convergence estimate and also an asymptotic formula in quantitative sense. In the end we present comparative study through graphical representation and propose an open problem.

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36

Bardaro, Carlo, and Ilaria Mantellini. "A Voronovskaya-Type Theorem for a General Class of Discrete Operators." Rocky Mountain Journal of Mathematics 39, no. 5 (October 2009): 1411–42. http://dx.doi.org/10.1216/rmj-2009-39-5-1411.

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37

Siddiqui, Mohammad Arif, and Raksha Rani Agrawal. "A Voronovskaya Type Theorem on Modified Post-Widder Operators Preserving x2." Kyungpook mathematical journal 51, no. 1 (March 31, 2011): 87–91. http://dx.doi.org/10.5666/kmj.2011.51.1.087.

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38

Qasim, Mohd, Mohammad Mursaleen, Asif Khan, and Zaheer Abbas. "Convergence of Generalized Lupaş-Durrmeyer Operators." Mathematics 8, no. 5 (May 24, 2020): 852. http://dx.doi.org/10.3390/math8050852.

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Анотація:

The main aim of this paper is to establish summation-integral type generalized Lupaş operators with weights of Beta basis functions which depends on μ having some properties. Primarily, for these new operators, we calculate moments and central moments, weighted approximation is discussed. Further, Voronovskaya type asymptotic theorem is proved. Finally, quantitative estimates for the local approximation is taken into consideration.

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39

Acar, Tuncer, Ali Aral, and Ioan Raşa. "Approximation by k-th order modifications of Szász—Mirakyan operators." Studia Scientiarum Mathematicarum Hungarica 53, no. 3 (September 2016): 379–98. http://dx.doi.org/10.1556/012.2016.53.3.1339.

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Анотація:

In this paper, we study the k-th order Kantorovich type modication of Szász—Mirakyan operators. We first establish explicit formulas giving the images of monomials and the moments up to order six. Using this modification, we present a quantitative Voronovskaya theorem for differentiated Szász—Mirakyan operators in weighted spaces. The approximation properties such as rate of convergence and simultaneous approximation by the new constructions are also obtained.

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40

Yilmaz, Ovgu Gurel, Vijay Gupta, and Ali Aral. "On Baskakov operators preserving the exponential function." Journal of Numerical Analysis and Approximation Theory 46, no. 2 (November 8, 2017): 150–61. http://dx.doi.org/10.33993/jnaat462-1110.

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Анотація:

In this paper, we are concerned about the King-type Baskakov operators defined by means of the preserving functions \(e_{0}\) and \(e^{2ax},\ a>0\) fixed. Using the modulus of continuity, we show the uniform convergence of new operators to \(f\). Also, by analyzing the asymptotic behavior of King-type operators with a Voronovskaya-type theorem, we establish shape preserving properties using the generalized convexity.

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41

Mursaleen, M., A. A. H. Al-Abied, and Khursheed Ansari. "On approximation properties of Baskakov-Schurer-Szász-Stancu operators based on q-integers." Filomat 32, no. 4 (2018): 1359–78. http://dx.doi.org/10.2298/fil1804359m.

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Анотація:

In the present paper, we introduce Stancu type generalization of Baskakov-Schurer-Sz?sz operators based on the q-integers and investigate their approximation properties. We obtain rate of convergence, weighted approximation and Voronovskaya type theorem for new operators. Then we obtain a point-wise estimate using the Lipschitz type maximal function. Furthermore, we study A-statistical convergence of these operators and also, in order to obtain a better approximation.

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42

Rempulska, L., and M. Skorupka. "The Voronovskaya theorem for some linear positive operators in exponential weight spaces." Publicacions Matemàtiques 41 (July 1, 1997): 519–26. http://dx.doi.org/10.5565/publmat_41297_16.

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43

ASLAN, Reşat. "Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\lambda$." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 2 (June 30, 2022): 407–21. http://dx.doi.org/10.31801/cfsuasmas.941919.

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Анотація:

In this paper, we study several approximation properties of Szasz-Mirakjan-Durrmeyer operators with shape parameter λ∈[−1,1]λ∈[−1,1]. Firstly, we obtain some preliminaries results such as moments and central moments. Next, we estimate the order of convergence in terms of the usual modulus of continuity, for the functions belong to Lipschitz type class and Peetre's K-functional, respectively. Also, we prove a Korovkin type approximation theorem on weighted spaces and derive a Voronovskaya type asymptotic theorem for these operators. Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.

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44

KARA, Mustafa. "Approximation properties of the fractional q-integral of Riemann-Liouville integral type Szasz-Mirakyan-Kantorovich operators." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 4 (December 30, 2022): 1135–67. http://dx.doi.org/10.31801/cfsuasmas.1067635.

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Анотація:

In the present paper, we introduce the fractional q-integral of Riemann-Liouville integral type Szász-Mirakyan-Kantorovich operators. Korovkin-type approximation theorem is given and the order of convergence of these operators are obtained by using Lipschitz-type maximal functions, second order modulus of smoothness and Peetre's K-functional. Weighted approximation properties of these operators in terms of modulus of continuity have been investigated. Then, for these operators, we give a Voronovskaya-type theorem. Moreover, bivariate fractional q- integral Riemann-Liouville fractional integral type Szász-Mirakyan-Kantorovich operators are constructed. The last section is devoted to detailed graphical representation and error estimation results for these operators.

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45

Deniz, Emre, Ali Aral, and Gulsum Ulusoy. "New integral type operators." Filomat 31, no. 9 (2017): 2851–65. http://dx.doi.org/10.2298/fil1709851d.

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Анотація:

In this paper we construct new integral type operators including heritable properties of Baskakov Durrmeyer and Baskakov Kantorovich operators. Results concerning convergence of these operators in weighted space and the hypergeometric form of the operators are shown. Voronovskaya type estimate of the pointwise convergence along with its quantitative version based on the weighted modulus of smoothness are given. Moreover, we give a direct approximation theorem for the operators in suitable weighted Lp space on [0,?).

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46

Sofyalıoğlu, Melek, and Kadir Kanat. "Approximation by Szász-Baskakov operators based on Boas-Buck-type polynomials." Filomat 36, no. 11 (2022): 3655–73. http://dx.doi.org/10.2298/fil2211655s.

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Анотація:

This paper concerns with a generalization of Sz?sz-Baskakov operators, which includes Boas-Buck-type polynomials. The convergence properties are studied in weighted space and the rate of convergence is obtained by using weighted modulus of continuity. A Voronovskaya-type theorem is investigated. Also, the theoretical results are demonstrated by choosing the particular cases of Boas-Buck-type polynomials, namely Appell polynomials, Hermite polynomials, Gould-Hopper polynomials, Laguerre polynomials and Charlier polynomials.

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47

Qasim, M., Asif Khan, Zaheer Abbas, Princess Raina, and Qing-Bo Cai. "Rate of Approximation for Modified Lupaş-Jain-Beta Operators." Journal of Function Spaces 2020 (August 3, 2020): 1–7. http://dx.doi.org/10.1155/2020/5090282.

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Анотація:

The main intent of this paper is to innovate a new construction of modified Lupaş-Jain operators with weights of some Beta basis functions whose construction depends on σ such that σ0=0 and infx∈0,∞σ′x≥1. Primarily, for the sequence of operators, the convergence is discussed for functions belong to weighted spaces. Further, to prove pointwise convergence Voronovskaya type theorem is taken into consideration. Finally, quantitative estimates for the local approximation are discussed.

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48

Bodur, Murat. "Modified Lupaş-Jain operators." Mathematica Slovaca 70, no. 2 (April 28, 2020): 431–40. http://dx.doi.org/10.1515/ms-2017-0361.

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Анотація:

Abstract The goal of this paper is to propose a modification of Lupaş-Jain operators based on a function ρ having some properties. Primarily, the convergence of given operators in weighted spaces is discussed. Then, order of approximation via weighted modulus of continuity is computed for these operators. Further, Voronovskaya type theorem in quantitative form is taken into consideration, as well. Ultimately, some graphical results that illustrate the convergence of investigated operators to f are given.

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49

Cheng, Wen-Tao, and S. A. Mohiuddine. "Construction of a new modification of Baskakov operators on (0,∞)." Filomat 37, no. 1 (2023): 139–54. http://dx.doi.org/10.2298/fil2301139c.

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Анотація:

In this manuscript, we construct new modification of Baskakov operators on (0,?) using the second central moment of the classical Baskakov operators. And the moments and the central moments computation formulas and their quantitative properties are computed. Then, rate of convergence, point-wise estimates, weighted approximation and Voronovskaya type theorem for the new operators are established. Also, Kantorovich and Durrmeyer type generalizations are discussed. Finally, some graphs and numerical examples are showed by using Matlab algorithms.

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50

Sucu, Sezgin, Gürhan İçöz, and Serhan Varma. "On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials." Abstract and Applied Analysis 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/680340.

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Анотація:

This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials.

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