Statistical approximation using wavelets Kantorovich (<i>p</i>,<i>q</i>)-Baskakov operators-Reference-Cited by-同舟云学术

Statistical approximation using wavelets Kantorovich (p,q)-Baskakov operators

Published:2023-11-30 Issue:0 Volume:0 Page:
ISSN:0174-4747
Container-title:Analysis
language:en
Short-container-title:

Author:

Moreka Alexander E.¹,Kumar Santosh²,Mursaleen M.³

Affiliation:

1. Department of Computer Systems and Mathematics , Ardhi Universty , Dar es Salaam ; and Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Dar es Salaam, Tanzania

2. Department of Mathematics , College of Natural and Applied Sciences , University of Dar es Salaam , Dar es Salaam , Tanzania ; and Department of Mathematics, North Eastern Hill University, Shillong, Meghalaya, India

3. Department of Medical Research , China Medical University Hospital , China Medical University (Taiwan) , Taichung , Taiwan ; and Department of Mathematics, Aligarh Muslim University, India

Abstract

Abstract The aim of this article is to construct a ( p , q )

{(p,q)}

-analogue of wavelets Kantorovich–Baskakov operators and investigate some statistical approximation properties. We study weighted statistical approximation by means of a Bohman–Korovkin-type theorem, and statistical rate of convergence by means of the weighted modulus of smoothness ω ρ α

{\omega_{\rho_{\alpha}}}

associated to the space B ρ ⁢ α ⁢ ( ℝ + )

{B_{\rho\alpha}(\mathbb{R_{+}})}

and Lipschitz-type maximal functions.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Numerical Analysis,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anly-2023-0028/pdf

Reference26 articles.

1. T. Acar, A. Aral and S. A. Mohiuddine, On Kantorovich modification of ( p , q ) (p,q) -Baskakov operators, J. Inequal. Appl. 2016 (2016), Paper No. 98.

2. F. Altomare and M. Campiti, Korovkin-Type Approximation Theory and its Applications, Walter de Gruyter, Berlin, 2011.

3. A. Aral and V. Gupta, On q-Baskakov type operators, Demonstr. Math. 42 (2009), no. 1, 109–122.

4. A. Aral and V. Gupta, ( p , q ) (p,q) -type beta functions of second kind, Adv. Oper. Theory 1 (2016), no. 1, 134–146.

5. A. Aral, V. Gupta and R. P. Agarwal, Applications of q-Calculus in Operator Theory, Springer, New York, 2013.