Generalized equi-statistical convergence of positive linear operators and associated approximation theorems
Reads0
Chats0
TLDR
The new notion of λ -equi-statistical convergence is applied to prove a Korovkin type approximation theorem and it is shown that the theorem is a non-trivial extension of some well-known Korovkins type approximation theorems.About:
This article is published in Mathematical and Computer Modelling.The article was published on 2012-05-01 and is currently open access. It has received 79 citations till now. The article focuses on the topics: Modes of convergence & Compact convergence.read more
Citations
More filters
Journal ArticleDOI
Weighted statistical convergence and its application to Korovkin type approximation theorem
TL;DR: This paper modify the definition of weighted statistical convergence and finds its relationship with the concept of statistical summability ( N ¯ , p n ) due to Moricz and Orhan (2004) to prove a Korovkin type approximation theorem.
Journal ArticleDOI
A Korovkin's type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean
TL;DR: A Korovkin type theorem is proved for the test functions 1, cosx,sinx in the space C"2"@p(R) of all continuous [email protected] functions on the real line R to prove the de la Vallee Poussin mean.
Journal ArticleDOI
Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems
TL;DR: In this paper, the authors introduced the notions of weighted lacunary statistical pointwise and uniform convergence and a kind of convergence which is lying between aforementioned convergence methods, and obtained various implication results with supporting examples.
Journal ArticleDOI
Operators constructed by means of q-Lagrange polynomials and A-statistical approximation
TL;DR: Some positive linear operators are constructed by means of q-Lagrange polynomials and some approximation results via A-statistical convergence are proved and defined by using the notion of modulus of continuity and Lipschitz class.
Journal ArticleDOI
Statistical summability ( C , 1 ) and a Korovkin type approximation theorem
TL;DR: The concept of statistical summability (C, 1) has been introduced by Moricz [Jour. Math. Anal. Appl. 275, 277-287 (2002)].
References
More filters
Journal ArticleDOI
On statistical convergence
TL;DR: In this article, it is shown that Statistical convergence cannot be included by any matrix metbod. And two Tauberian theorems are proved: one uses the Tauberians condition Axi, = 0(1/Ar), which is shown to be ''best possible,\" and the other is concerned with gap sequences.