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Автор: Grafiati

Опубліковано: 11 вересня 2023

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1

Pethe, S. "Corrigendum: ‘On Linear Positive Operators’." Journal of the London Mathematical Society s2-40, no. 2 (October 1989): 267–68. http://dx.doi.org/10.1112/jlms/s2-40.2.267-s.

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2

Özarslan, Mehmet. "q -Laguerre type linear positive operators." Studia Scientiarum Mathematicarum Hungarica 44, no. 1 (March 1, 2007): 65–80. http://dx.doi.org/10.1556/sscmath.44.2007.1.7.

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Анотація:

The main object of this paper is to define the q -Laguerre type positive linear operators and investigate the approximation properties of these operators. The rate of convegence of these operators are studied by using the modulus of continuity, Peetre’s K -functional and Lipschitz class functional. The estimation to the difference | Mn +1, q ( ƒ ; χ )− Mn , q ( ƒ ; χ )| is also obtained for the Meyer-König and Zeller operators based on the q -integers [2]. Finally, the r -th order generalization of the q -Laguerre type operators are defined and their approximation properties and the rate of convergence of this r -th order generalization are also examined.

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3

Popa, Dorian, and Ioan Raşa. "Steklov averages as positive linear operators." Filomat 30, no. 5 (2016): 1195–201. http://dx.doi.org/10.2298/fil1605195p.

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4

Duman, O., and C. Orhan. "Statistical approximation by positive linear operators." Studia Mathematica 161, no. 2 (2004): 187–97. http://dx.doi.org/10.4064/sm161-2-6.

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5

Park, Choon-Kil, and Jong-Su An. "POSITIVE LINEAR OPERATORS IN C*-ALGEBRAS." Bulletin of the Korean Mathematical Society 46, no. 5 (September 30, 2009): 1031–40. http://dx.doi.org/10.4134/bkms.2009.46.5.1031.

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6

Gadjiev, Akif, Oktay Duman, and A. M. Ghorbanalizadeh. "Ideal Convergence ofk-Positive Linear Operators." Journal of Function Spaces and Applications 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/178316.

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Анотація:

We study some ideal convergence results ofk-positive linear operators defined on an appropriate subspace of the space of all analytic functions on a bounded simply connected domain in the complex plane. We also show that our approximation results with respect to ideal convergence are more general than the classical ones.

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7

Demirci, Kamil, and Sevda Karakuş. "StatisticalA-summability of positive linear operators." Mathematical and Computer Modelling 53, no. 1-2 (January 2011): 189–95. http://dx.doi.org/10.1016/j.mcm.2010.08.003.

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8

Atlihan, Ö. G., and C. Orhan. "Summation process of positive linear operators." Computers & Mathematics with Applications 56, no. 5 (September 2008): 1188–95. http://dx.doi.org/10.1016/j.camwa.2008.02.020.

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9

Gavrea, I., H. H. Gonska, and D. P. Kacsó. "Positive linear operators with equidistant nodes." Computers & Mathematics with Applications 32, no. 8 (October 1996): 23–32. http://dx.doi.org/10.1016/0898-1221(96)00163-0.

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10

Atlihan, Özlem G., and Cihan Orhan. "Matrix Summability and Positive Linear Operators." Positivity 11, no. 3 (August 2007): 387–98. http://dx.doi.org/10.1007/s11117-007-2049-y.

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11

Daners, Daniel, Jochen Glück, and James B. Kennedy. "Eventually positive semigroups of linear operators." Journal of Mathematical Analysis and Applications 433, no. 2 (January 2016): 1561–93. http://dx.doi.org/10.1016/j.jmaa.2015.08.050.

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12

Xiao, Wei. "Approximation Strategy by Positive Linear Operators." Journal of Function Spaces and Applications 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/856084.

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13

Aral, Ali, Daniela Inoan, and Ioan Raşa. "On differences of linear positive operators." Analysis and Mathematical Physics 9, no. 3 (April 12, 2018): 1227–39. http://dx.doi.org/10.1007/s13324-018-0227-7.

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14

Makin, R. S. "A class of linear positive operators." Mathematical Notes of the Academy of Sciences of the USSR 43, no. 1 (January 1988): 43–48. http://dx.doi.org/10.1007/bf01139568.

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15

Volkov, Yu I. "Multisequences of multidimensional positive linear operators." Ukrainian Mathematical Journal 36, no. 3 (1985): 257–62. http://dx.doi.org/10.1007/bf01077457.

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16

Acu, Ana Maria, Sever Hodiş, and Ioan Rașa. "Estimates for the Differences of Certain Positive Linear Operators." Mathematics 8, no. 5 (May 14, 2020): 798. http://dx.doi.org/10.3390/math8050798.

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Анотація:

The present paper deals with estimates for differences of certain positive linear operators defined on bounded or unbounded intervals. Our approach involves Baskakov type operators, the kth order Kantorovich modification of the Baskakov operators, the discrete operators associated with Baskakov operators, Meyer–König and Zeller operators and Bleimann–Butzer–Hahn operators. Furthermore, the estimates in quantitative form of the differences of Baskakov operators and their derivatives in terms of first modulus of continuity are obtained.

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17

Attalienti, Antonio, and Ioan Raşa. "The eigenstructure of some positive linear operators." Journal of Numerical Analysis and Approximation Theory 43, no. 1 (February 1, 2014): 45–58. http://dx.doi.org/10.33993/jnaat431-994.

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Анотація:

Of concern is the study of the eigenstructure of some classes of positive linear operators satisfying particular conditions. As a consequence, some results concerning the asymptotic behaviour as \(t\to +\infty\) of particular strongly continuous semigroups \((T(t))_{t\geq 0}\) expressed in terms of iterates of the operators under consideration are obtained as well. All the analysis carried out herein turns out to be quite general and includes some applications to concrete cases of interest, related to the classical Beta, Stancu and Bernstein operators.

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18

Păcurar, Cristina, and Radu Păltănea. "Approximation of generalized nonlinear Urysohn operators using positive linear operators." Filomat 35, no. 8 (2021): 2595–604. http://dx.doi.org/10.2298/fil2108595p.

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Анотація:

There are presented two methods for approximation of generalized Urysohn type operators. The first of them is the natural generalization of the method considered first by Demkiv in [1]. The convergence results are given in quantitative form, using certain moduli of continuity. In the final part there are given a few exemplifications for discrete and integral type operators and, in particular, for Bernstein and Durrmeyer operators.

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19

Nussbaum, Roger. "Periodic points of positive linear operators and Perron-Frobenius operators." Integral Equations and Operator Theory 39, no. 1 (March 2001): 41–97. http://dx.doi.org/10.1007/bf01192149.

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20

Lupaş, Aleandru, та Detlef H. Mache. "TheΘ-transformation of certain positive linear operators". International Journal of Mathematics and Mathematical Sciences 19, № 4 (1996): 667–78. http://dx.doi.org/10.1155/s0161171296000932.

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Анотація:

The intention of this paper is to describe a construction method for a new sequence of linear positive operators, which enables us to get a pointwise order of approximation regarding the polynomial summator operators which have best properties of approximation.

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21

Hodiş, Sever. "Differences and quotients of positive linear operators." General Mathematics 28, no. 2 (December 1, 2020): 81–85. http://dx.doi.org/10.2478/gm-2020-0017.

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Анотація:

Abstract We consider the classical Szász-Mirakyan and Szász-Mirakyan-Durrmeyer operators, as well as a Kantorovich modification and a discrete version of it. The images of exponential functions under these operators are determined. We establish estimates involving differences and quotients of these images.

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22

AREMU, Saheed Olaosebikan, and Ali OLGUN. "On difference of bivariate linear positive operators." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 3 (September 30, 2022): 791–805. http://dx.doi.org/10.31801/cfsuasmas.992524.

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Анотація:

In the present paper we give quantitative type theorems for the differences of different bivariate positive linear operators by using weighted modulus of continuity. Similar estimates are obtained via K-functional and for Chebyshev functionals. Moreover, an example involving Szasz and Szasz-Kantorovich operators is given.

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23

Gazanfer, Afşin Kürşat, and İbrahim Büyükyazıcı. "Approximation by Certain Linear Positive Operators of Two Variables." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/782080.

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Анотація:

We introduce positive linear operators which are combined with the Chlodowsky and Szász type operators and study some approximation properties of these operators in the space of continuous functions of two variables on a compact set. The convergence rate of these operators are obtained by means of the modulus of continuity. And we also obtain weighted approximation properties for these positive linear operators in a weighted space of functions of two variables and find the convergence rate for these operators by using the weighted modulus of continuity.

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24

Acu, Ana-Maria, Gülen Başcanbaz-Tunca, and Ioan Rasa. "Differences of Positive Linear Operators on Simplices." Journal of Function Spaces 2021 (March 25, 2021): 1–11. http://dx.doi.org/10.1155/2021/5531577.

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Анотація:

The aim of the paper is twofold: we introduce new positive linear operators acting on continuous functions defined on a simplex and then estimate differences involving them and/or other known operators. The estimates are given in terms of moduli of smoothness and K -functionals. Several applications and examples illustrate the general results.

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25

Dhamija, Minakshi, and Naokant Deo. "Approximation by generalized positive linear Kantorovich operators." Filomat 31, no. 14 (2017): 4353–68. http://dx.doi.org/10.2298/fil1714353d.

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Анотація:

In the present article, we introduce generalized positive linear-Kantorovich operators depending on P?lya-Eggenberger distribution (PED) as well as inverse P?lya-Eggenberger distribution (IPED) and for these operators, we study some approximation properties like local approximation theorem, weighted approximation and estimation of rate of convergence for absolutely continuous functions having derivatives of bounded variation.

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26

Sharma, Prerna. "Approximation by Some Stancu Type Linear Positive Operators." Journal of Nepal Mathematical Society 5, no. 2 (December 20, 2022): 34–41. http://dx.doi.org/10.3126/jnms.v5i2.50017.

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Анотація:

Present paper is the study about Stancu type generalization of modified Beta-Szasz operators and their q-analogues. We obtain some approximation properties for these operators and estimate the rate of convergence by using the first and second order modulus of continuity. Author also investigates the statistical approximation properties of the q-Beta-Stancu operators using Korokvin theorem.

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27

Cao, Haisong. "Improved Young's inequalities for positive linear operators." ScienceAsia 46, no. 2 (2020): 224. http://dx.doi.org/10.2306/scienceasia1513-1874.2020.020.

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28

Cao, Haisong. "Improved Young's inequalities for positive linear operators." ScienceAsia 46, no. 2 (2020): 224. http://dx.doi.org/10.2306/scienceasia1513-1874.2020.46.224.

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29

Gavrea, Ioan, and Mircea Ivan. "On the iterates of positive linear operators." Journal of Approximation Theory 163, no. 9 (September 2011): 1076–79. http://dx.doi.org/10.1016/j.jat.2011.02.012.

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30

Deo, Naokant, and Minakshi Dhamija. "Charlier–Szász–Durrmeyer type positive linear operators." Afrika Matematika 29, no. 1-2 (October 23, 2017): 223–32. http://dx.doi.org/10.1007/s13370-017-0537-1.

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31

Ostrovska, Sofiya. "Positive linear operators generated by analytic functions." Proceedings Mathematical Sciences 117, no. 4 (November 2007): 485–93. http://dx.doi.org/10.1007/s12044-007-0040-y.

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32

Karakuş, Sevda, Kamil Demirci, and Oktay Duman. "Equi-statistical convergence of positive linear operators." Journal of Mathematical Analysis and Applications 339, no. 2 (March 2008): 1065–72. http://dx.doi.org/10.1016/j.jmaa.2007.07.050.

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33

Meyer, Ralf. "The Carathéodory Pseudodistance and Positive Linear Operators." International Journal of Mathematics 08, no. 06 (September 1997): 809–24. http://dx.doi.org/10.1142/s0129167x97000408.

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Анотація:

We give a new elementary proof of Lempert's theorem, which states that for convex domains the Carathéodory pseudodistance coincides with the Lempert function and thus with the Kobayashi pseudodistance. Moreover, we prove the product property of the Carathéodory pseudodistance. Our methods are functional analytic and work also in the more general setting of uniform algebras.

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34

Dăneţ, Nicolae, and Rodica-Mihaela Dăneţ. "Existence and extensions of positive linear operators." Positivity 13, no. 1 (April 30, 2008): 89–106. http://dx.doi.org/10.1007/s11117-008-2220-0.

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35

Yılmaz, Burçak, Kamil Demirci, and Sevda Orhan. "Relative modular convergence of positive linear operators." Positivity 20, no. 3 (October 1, 2015): 565–77. http://dx.doi.org/10.1007/s11117-015-0372-2.

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36

Yang, Mingze. "Completely positive linear operators for Banach spaces." International Journal of Mathematics and Mathematical Sciences 17, no. 1 (1994): 27–30. http://dx.doi.org/10.1155/s0161171294000049.

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Анотація:

Using ideas of Pisier, the concept of complete positivity is generalized in a different direction in this paper, where the Hilbert spaceℋis replaced with a Banach space and its conjugate linear dual. The extreme point results of Arveson are reformulated in this more general setting.

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37

Mahmudov, N. I. "Approximation theorems for certain positive linear operators." Applied Mathematics Letters 23, no. 7 (July 2010): 812–17. http://dx.doi.org/10.1016/j.aml.2010.03.016.

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38

Demirci, Kamil, та Fadime Dirik. "Statistical σ-convergence of positive linear operators". Applied Mathematics Letters 24, № 3 (березень 2011): 375–80. http://dx.doi.org/10.1016/j.aml.2010.10.031.

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39

Gupta, Vijay. "A large family of linear positive operators." Rendiconti del Circolo Matematico di Palermo Series 2 69, no. 3 (June 20, 2019): 701–9. http://dx.doi.org/10.1007/s12215-019-00430-3.

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40

Khan, M. Kazim, B. Della Vecchia, and A. Fassih. "On the Monotonicity of Positive Linear Operators." Journal of Approximation Theory 92, no. 1 (January 1998): 22–37. http://dx.doi.org/10.1006/jath.1996.3113.

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41

Acu, Ana Maria, Ioan Raşa, and Andra Seserman. "Composition and Decomposition of Positive Linear Operators (VIII)." Axioms 12, no. 3 (February 22, 2023): 228. http://dx.doi.org/10.3390/axioms12030228.

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Анотація:

In a series of papers, most of them authored or co-authored by H. Gonska, several authors investigated problems concerning the composition and decomposition of positive linear operators defined on spaces of functions. For example, given two operators with known properties, A and B, we can find the properties of the composed operator A∘B, such as the eigenstructure, the inverse, the Voronovskaja formula, and the second-order central moments. One motivation for studying composed operators is the possibility to obtain better rates of approximation and better Voronovskaja formulas. Our paper will address such problems involving compositions of some classical positive linear operators. We present general results as well as numerical experiments.

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42

Wood, B. "Order of approximation by linear combinations of positive linear operators." Journal of Approximation Theory 45, no. 4 (December 1985): 375–82. http://dx.doi.org/10.1016/0021-9045(85)90033-4.

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43

Kacsó, Daniela. "Estimates for Iterates of Positive Linear Operators Preserving Linear Functions." Results in Mathematics 54, no. 1-2 (July 14, 2009): 85–101. http://dx.doi.org/10.1007/s00025-009-0363-3.

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44

Gonska, Heiner, and Ioan Raşa. "On infinite products of positive linear operators reproducing linear functions." Positivity 17, no. 1 (December 7, 2011): 67–79. http://dx.doi.org/10.1007/s11117-011-0149-1.

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45

Patel, Prashantkumar. "Some approximation properties of new families of positive linear operators." Filomat 33, no. 17 (2019): 5477–88. http://dx.doi.org/10.2298/fil1917477p.

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Анотація:

In the present article, we propose the new class positive linear operators, which discrete type depending on a real parameters. These operators are similar to Jain operators but its approximation properties are different then Jain operators. Theorems of degree of approximation, direct results, Voronovskaya Asymptotic formula and statistical convergence are discussed.

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46

Birou, Marius-Mihai. "Quantitative results for positive linear operators which preserve certain functions." General Mathematics 27, no. 2 (December 1, 2019): 85–95. http://dx.doi.org/10.2478/gm-2019-0017.

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Анотація:

AbstractIn this paper we obtain estimations of the errors in approximation by positive linear operators which fix certain functions. We use both the first and the second order classical moduli of smoothness and a generalized modulus of continuity of order two. Some applications involving Bernstein type operators, Kantorovich type operators and genuine Bernstein-Durrmeyer type operators are presented.

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47

Pop, Ovidiu T. "About Some Linear Operators." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–13. http://dx.doi.org/10.1155/2007/91781.

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Анотація:

Using the method of Jakimovski and Leviatan from their work in 1969, we construct a general class of linear positive operators. We study the convergence, the evaluation for the rate of convergence in terms of the first modulus of smoothness and we give a Voronovskaja-type theorem for these operators.

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48

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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49

Gonska, Heiner, and Ioan Raşa. "On the composition and decomposition of positive linear operators (II)." Studia Scientiarum Mathematicarum Hungarica 47, no. 4 (December 1, 2010): 448–61. http://dx.doi.org/10.1556/sscmath.2009.1144.

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Анотація:

This note discusses the indecomposability and decomposability of certain operators occurring frequently in approximation theory: piecewise linear interpolation and Bernsteintype operators. The second topic includes the central (absolute) moments of the composition of two operators and their asymptotic behavior.

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50

Gupta, Vijay, Ana Maria Acu, and Hari Mohan Srivastava. "Difference of Some Positive Linear Approximation Operators for Higher-Order Derivatives." Symmetry 12, no. 6 (June 2, 2020): 915. http://dx.doi.org/10.3390/sym12060915.

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Анотація:

In the present paper, we deal with some general estimates for the difference of operators which are associated with different fundamental functions. In order to exemplify the theoretical results presented in (for example) Theorem 2, we provide the estimates of the differences between some of the most representative operators used in Approximation Theory in especially the difference between the Baskakov and the Szász–Mirakyan operators, the difference between the Baskakov and the Szász–Mirakyan–Baskakov operators, the difference of two genuine-Durrmeyer type operators, and the difference of the Durrmeyer operators and the Lupaş–Durrmeyer operators. By means of illustrative numerical examples, we show that, for particular cases, our result improves the estimates obtained by using the classical result of Shisha and Mond. We also provide the symmetry aspects of some of these approximations operators which we have studied in this paper.

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