Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems

被引：0
作者：
S. A. Mohiuddine
Badriah A. S. Alamri
机构：
[1] King Abdulaziz University,Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2019年 / 113卷
关键词：
Weighted lacunary equi-statistical convergence; Korovkin-type approximation theorems; Positive linear operators; Rate of convergence; Voronovskaya-type theorem; 40G15; 40A30; 41A25; 41A36;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We introduce the notions of weighted lacunary statistical pointwise and uniform convergence and a kind of convergence which is lying between aforementioned convergence methods, namely, weighted lacunary equi-statistical convergence and obtain various implication results with supporting examples. We then apply our new concept of weighted lacunary equi-statistical convergence with a view to proving Korovkin and Voronovskaya type approximation theorems. We also construct an example with the help of generating functions type Meyer-König and Zeller which shows that our Korovkin-type theorem is stronger than its classical version. Moreover, we compute the rate of weighted lacunary equi-statistical convergence for operators in terms of modulus of continuity.
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页码：1955 / 1973
页数：18
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