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

Journal of inequalities and applications

Tarul Garg¹ 

关键词: Brenke type polynomials;    Szász operator;    Ditzian-Totik modulus of smoothness;    derivative of bounded variation;    Peetre’s K-functional;    rate of convergence;    41A10;    41A25;    41A36;   

DOI  :  10.1186/s13660-017-1430-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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】

CC BY