Approximation by bivariate Chlodowsky type Szász–Durrmeyer operators and associated GBS operators on weighted spaces

Journal of Inequalities and Applications

Reşat Aslan¹  M. Mursaleen² 

[1] Department of Mathematics, Faculty of Sciences and Arts, Harran University, 63100, Şanlıurfa, Turkey;Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan;Department of Mathematics, Aligarh Muslim University, 202002, Aligarh, India;

关键词: Weighted approximation;    Mixed modulus of continuity;    Lipschitz type functions;    GBS type operators;    Degree of approximation;    41A10;    41A25;    41A35;   

DOI  :  10.1186/s13660-022-02763-7

来源: Springer

【 摘 要 】

In this article, we consider a bivariate Chlodowsky type Szász–Durrmeyer operators on weighted spaces. We obtain the rate of approximation in connection with the partial and complete modulus of continuity and also for the elements of the Lipschitz type class. Moreover, we examine the degree of convergence with regard to the weighted modulus of continuity and Peetre’s K-functional. Further, we construct the associated GBS type of these operators and estimate the degree of approximation using the mixed modulus of continuity and a class of the Lipschitz of Bögel type continuous functions. Finally, with the help of Maple software, we present the comparisons of the convergence of the bivariate Chlodowsky type Szász–Durrmeyer operators and associated GBS type operators to certain functions with some graphs and error estimation tables.

【 授权许可】

CC BY