Some classes of ideal convergent sequences and generalized difference matrix operator

Abstract

The aim of paper is to define and study some ideal convergent sequence spaces with the help of generalized difference matrix B n (m) and Orlicz functions. We also make an effort to study some algebraic and topological properties of these difference sequence spaces.

Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces

“…Let 1 > 0, 2 > 0 and = max{1, 1 , 2 }, since is Orlicz function and by using (22), (23), and (24), we have…”

Some Seminormed Difference Sequence Spaces over n-Normed Spaces Defined by a Musielak-Orlicz Function of Order (α,β)

“…For recent work related to various kinds of difference sequence spaces, we refer to [7][8][9][10][11][12][13] and references therein.…”

Generalized Statistical Convergence of Double Sequences in Paranormed Spaces

“…Mursaleen [24] presented a generalization of statistical convergence with the help of non-decreasing sequence λ = (λ k ) such that λ k+1 ≤ λ k + 1 and λ 1 = 0 of positive numbers tending to ∞ and called it λ-statistical convergence. We also refer to the recent work in [1,3,4,6,7,10,14,17,18,21,22] for some applications of convergence methods to approximation theorems. Pringsheim [29] extended the notion of usual convergence from single sequences of real numbers to double sequences as follows: A double sequence x = (x jk ) has a Pringsheim limit ξ (convergent to ξ in Pringsheim's sense), in symbols, we shall write (P ) lim x = ξ, provided that given an > 0 there exists an N ∈ N such that |x jk − ξ| < whenever…”