Weighted almost convergence and related infinite matrices

Abstract

The purpose of this paper is to introduce the notion of weighted almost convergence of a sequence and prove that this sequence endowed with the sup-norm is a BK-space. We also define the notions of weighted almost conservative and regular matrices and obtain necessary and sufficient conditions for these matrix classes. Moreover, we define a weighted almost A-summable sequence and prove the related interesting result.

On i-convergent sequence spaces defined by Jordan totient operator

“…Many authors have extensively developed the theory of the matrix transformations between some sequence spaces. Interested readers can refer to [10,19,21,22,28] and references therein.…”

Compact operators on the Jordan totient sequence spaces

“…The study of domains of special matrices has been a great interest over years. For more details about the theory of sequence spaces and applications of summability theory, we refer to other studies 1-10 …”

“…For more details about the theory of sequence spaces and applications of summability theory, we refer to other studies. [1][2][3][4][5][6][7][8][9][10] A sequence space is a linear subspace of the set of all real valued sequences . Some of the classical sequence spaces are…”

A new paranormed sequence space defined by Catalan conservative matrix

“…For the literature review, one can refer to previous studies [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] about normed spaces and paranormed spaces derived by domains of special infinite matrices.…”