On the order of approximation by modified summation-integral-type operators based on two parameters-Reference-Cited by-同舟云学术

On the order of approximation by modified summation-integral-type operators based on two parameters

Published:2023-01-01 Issue:1 Volume:56 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Mohiuddine Syed Abdul¹²,Singh Karunesh Kumar³,Alotaibi Abdullah¹

Affiliation:

1. Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University , Jeddah 21589 , Saudi Arabia

2. Department of General Required Courses, Mathematics, The Applied College, King Abdulaziz University , Jeddah 21589 , Saudi Arabia

3. Department of Applied Sciences and Humanities, Institute of Engineering and Technology, Dr. A. P. J. Abdul Kalam Technical University, Sitapur Road , Lucknow 226021 , Uttar Pradesh , India

Abstract

Abstract In this article, we the study generalized family of positive linear operators based on two parameters, which are a broad family of many well-known linear positive operators, e.g., Baskakov-Durrmeyer, Baskakov-Szász, Szász-Beta, Lupaş-Beta, Lupaş-Szász, genuine Bernstein-Durrmeyer, and Pǎltǎnea. We first find direct estimates in terms of the second-order modulus of continuity, then we find an estimate of error in the Ditzian-Totik modulus of smoothness. Then we discuss the rate of approximation for functions in the Lipschitz class. Furthermore, we study the pointwise Grüss-Voronovskaja-type result and also establish the Grüss-Voronovskaja-type asymptotic formula in quantitative form.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2022-0182/pdf

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