Generalized weighted statistical convergence of double sequences and applications

Abstract

In this paper we introduce the concept generalized weighted statistical convergence of double sequences. Some relations between weighted (?,?)-statistical convergence and strong (N???,p,q,?,?)-summablity of double sequences are examined. Furthemore, we apply our new summability method to prove a Korovkin type theorem.

Tauberian theorems for weighted mean statistical summability of double sequences of fuzzy numbers

“…It follows from Theorem 2.6 of [6] and Example 4.2 of [19] that the converse implication of Theorem 2.4 does not hold in general. We nd some conditions under which the converse also holds.…”

Influence of θ-metric spaces on the diameter of rough weighted I2-limit set

“…In this section we recall some of the basic concepts of ideal, filter, rough I 2 -convergence, weighted statistical convergence for double sequence and θ-metric space. Interested readers can look into [5,6,17,19] for details. Definition 2.1.…”

“…Definition 2.6. [6]. Let p = {p m } m∈N and q = {q n } n∈N be sequences of real numbers such that lim inf…”

αβ-WEIGHTED dg-STATISTICAL CONVERGENCE IN PROBABILITY

“…Another generalization of the statistical convergence is known as weighted statistical convergence which was established by Karakaya and Chishti [20] in 2009 and gradually improved by Aizpuru et al [2], Cinar and Et [6,12], Das et al [9], Ghosal [16][17][18], Işik and Altin [19], Mursaleen et al [22] and Som [25].…”