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Добірка наукової літератури з теми "VORONOVSKAYA THEOREM"

Автор: Grafiati

Опубліковано: 26 жовтня 2023

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Статті в журналах з теми "VORONOVSKAYA THEOREM"

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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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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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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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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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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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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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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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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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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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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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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Більше джерел

Дисертації з теми "VORONOVSKAYA THEOREM"

MISHRA, NAV SHAKTI. "A STUDY ON ESTIMATES OF CONVERGENCE OF CERTAIN APPROXIMATION OPERATORS." Thesis, 2023. http://dspace.dtu.ac.in:8080/jspui/handle/repository/19752.

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Анотація:

This thesis is mainly a study of convergence estimates of various approximation opera tors. Approximation theory is indeed an old topic in mathematical analysis that remains an appealing field of study with several applications. The findings presented here are related to the approximation of specific classes of linear positive operators. The introduc tory chapter is a collection of relevant definitions and literature of concepts that are used throughout this thesis. The second chapter is based on approximation of certain exponential type opera tors. The first section of this chapter presents the study of convergence estimates of Kan torovich variant of Ismail-May operators. Further, a two variable generalisation of the proposed operators is also discussed. The second section is dedicated to a modification of Ismail-May exponential type operators which preserve functions of exponential growth. The modified operators in general are not of exponential type. In chapter three, we present a Durrmeyer type construction involving a class of or thogonal polynomials called Apostol-Genocchi polynomials and Palt ˇ anea operators with ˇ real parameters α, λ and ρ. We establish approximation estimates such as a global approx imation theorem and rate of approximation in terms of usual, r−th and weighted modulus of continuity. We further study asymptotic formulae such as Voronovskaya theorem and quantitative Voronovskaya theorem. The rate of convergence of the proposed operators for the functions whose derivatives are of bounded variation is also presented. Inspired by the King’s approach, chapter four deals with the preservation of func tions of the form t s , s ∈ N ∪ {0}. Followed by some useful lemmas, we determine the rate of convergence of the proposed operators in terms of usual modulus of continuity and Peetre’s K- functional. Further, the degree of approximation is also established for the function of bounded variation. We also illustrate via figures and tables that the proposed modification provides better approximation for preservation of test function e3. In chapter five, we consider a Kantorovich variant of the operators proposed by Gupta and Holhos (68) using arbitrary sequences which preserves the exponential func tions of the form a −x . It is shown that the order of approximation can be made better xi xii Abstract with appropriate choice of sequences with certain conditions. We therefore provide nec essary moments and central moments and some useful lemmas. Further, we present a quantitative asymptotic formula and estimate the error in approximation. Graphical rep resentations are provided in the end with different choices of sequences satisfying the given conditions. The last chapter summarizes the thesis with a brief conclusion and also discusses the future prospects of this thesis.

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Частини книг з теми "VORONOVSKAYA THEOREM"

Vedi, Tuba, and Mehmet Ali Özarslan. "Voronovskaja Type Approximation Theorem for q-Szasz–Schurer Operators." In Springer Proceedings in Mathematics & Statistics, 353–61. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28443-9_25.

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Anastassiou, George A., and Merve Kester. "Voronovskaya Type Asymptotic Expansions for Multivariate Generalized Discrete Singular Operators." In Intelligent Mathematics II: Applied Mathematics and Approximation Theory, 233–44. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30322-2_16.

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"Voronovskaya Like Asymptotic Expansions for Generalized Discrete Singular Operators." In Discrete Approximation Theory, 51–64. World Scientific, 2016. http://dx.doi.org/10.1142/9789813145849_0003.

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"Voronovskaya Like Asymptotic Expansions for Multivariate Generalized Discrete Singular Operators." In Discrete Approximation Theory, 239–52. World Scientific, 2016. http://dx.doi.org/10.1142/9789813145849_0009.

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