Polynomial Weighted Approximation by Szász-Mirakyan Operators of Max-product type


Download PDF

Authors: E. ACAR, A. HOLHOS AND S. K. SERENBAY

DOI: 10.46793/KgJMat2503.365A

Abstract:

In this paper, we study approximation of Szász-Mirakyan operators of max-product type in polynomial weighted spaces. We reckon the rate of approximation in terms of some exponential weighted spaces for obtain a better rate of approximation than the corresponding positive linear operators.



Keywords:

Szász-Mirakyan operators, weighted modulus of continuity, weighted approximation



References:

[1]   A. Holhoş, Uniform weighted approximation by positive linear operators, Stud. Univ. Babeş-Bolyai Math. 56(3) (2011), 135–146.

[2]   B. Bede, L. Coroianu and S. G. Gal, Approximation by Max-Product Type Operators, Springer International Publishing, Switzerland, 2016.

[3]   B. Bede, L. Coroianu and S. G. Gal, Approximation and shape preserving properties of the nonlinear Favard-Szász-Mirakyan operator of max-product type, Filomat 24(3) (2010), 55–72. https://doi.org/10.2298/FIL1003055B

[4]   B. Bede and S. G. Gal, Approximation by nonlinear Bernstein and Favard-Szász-Mirakyan operators of max-product kind, Journal of Concrete and Applicable Mathematics 8(2) (2010), 193–207.

[5]    A. Holhoş, Approximation of functions by Favard-Szász-Mirakyan operator of max-product type in weighted spaces, Filomat 32(7) (2017), 2567–2576. https://doi.org/10.2298/FIL1807567H

[6]   A. Holhoş, Weighted approximation of functions by Meyer-König and Zeller operators of max-product type, Numer. Funct. Anal. Optim. 39(6) (2018), 689–703. https://doi.org/10.1080/01630563.2017.1413386

[7]   V. Totik, Uniform approximation by Szász-Mirakjan type operators, Acta Math. Hungar. 41(3) (1983), 291–307.

[8]   A. Holhoş, Quantitative estimates of Voronovskaya type in weighted spaces, Results Math. 73(2) (2018), 52–73. https://doi.org/10.1007/s00025-018-0814-9

[9]   O. Szasz, Generalization of Bernstein’s polynomials to the infinite interval, Journal of Research of the National Bureau of Standards 45(3) (1950), 239—245.