Rate of convergence by Kantorovich-Szász type operators based on Brenke type polynomials

Journal of Inequalities and Applications

Serkan Araci¹  Tarul Garg²  Purshottam Narain Agrawal² 

[1] Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University;Department of Mathematics, Indian Institute of Technology Roorkee;

关键词: Brenke type polynomials;    Szász operator;    Ditzian-Totik modulus of smoothness;    derivative of bounded variation;    Peetre’s K-functional;    rate of convergence;   

DOI  :  10.1186/s13660-017-1430-z

来源: DOAJ

【 摘 要 】

Abstract The present paper deals with the approximation properties of the univariate operators which are the generalization of the Kantorovich-Szász type operators involving Brenke type polynomials. We investigate the order of convergence by using Peetre’s K-functional and the Ditzian-Totik modulus of smoothness and study the degree of approximation of the univariate operators for continuous functions in a Lipschitz space, a Lipschitz type maximal function and a weighted space. The rate of approximation of functions having derivatives equivalent with a function of bounded variation is also obtained.

【 授权许可】

Unknown