Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators

Journal of inequalities and applications

Shahid Ahmad Wani¹  Kottakkaran Sooppy Nisar²  M. Mursaleen³ 

[1] Department of CSE, North Campus, University of Kashmir, Srinagar, India;Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, 11991, Wadi Aldawser, Saudi Arabia;Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan;Al-Qaryah, Doharra, Street No. 1 (West), 202002, Aligarh, UP, India;

关键词: Szasz operators;    Brenke type polynomials;    Jakimovski–Leviatan operators;    Modulus of continuity;    Weighted space;    40A30;    41A10;    41A25;    41A36;   

DOI  :  10.1186/s13660-021-02639-2

来源: Springer

【 摘 要 】

In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also considered. Finally, the Voronovskaya type theorem is demonstrated for some particular case of these polynomials.

【 授权许可】

CC BY