A new construction of Lupaş operators and its approximation properties

Advances in Difference Equations

article

Qasim, Mohd¹  Khan, Asif²  Abbas, Zaheer¹  Cai, Qing-Bo³ 

[1] Department of Mathematical Sciences, Baba Ghulam Shah Badshah University;Department of Mathematics, Aligarh Muslim University;School of Mathematics and Computer Science, Quanzhou Normal University

关键词: Positive operators;    Voronovskaya-type theorem;    Weighted modulus of continuity;    Local approximation;   

DOI  :  10.1186/s13662-020-03143-5

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences$u_{m} $ and$v_{m}$ of functions. We prove that the new operators provide better weighted uniform approximation over$[0,\infty )$ . In terms of weighted moduli of smoothness, we obtain degrees of approximation associated with the function ρ. Also, we prove Voronovskaya-type theorem, quantitative estimates for the local approximation.

【 授权许可】

CC BY