A Novel Generalized Difference Spaces Constructed by the Modulus Function

Year 2018, Volume: 6 Issue: 1, 17 - 25, 15.04.2018

Murat Candan , İhsan Solak

Abstract

A major role of this document is to present a generalized difference spaces denoted by $w(\Delta ^{r},\hat{A},p,f,q,s),$ $w_{0}(\Delta ^{r},\hat{A},p,f,q,s),$ and $w_{\infty}(\Delta ^{r},\hat{A},p,f,q,s)$, of which arguments are defined as follows, and also to investigate some algebraic and topological characteristics of the spaces. Here; $\hat{A}$ is an infinite matrix, $p=(p_{k})$ is a bounded sequence of strictly positive real numbers, $f$ is any modulus function, $q$ is a semi norm, and $s$ is any non-negative real number. Besides these, the relationship between the spaces obtained by various values of those arguments is going to be considered. Finally, the newly obtained results are going to be compared with those of other studies.

Keywords

Difference sequence spaces, modulus function

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