Application of the infinite matrix theory to the solvability of certain sequence spaces equations with operators

Abstract

In this paper we deal with special {ıt sequence spaces equations (SSE)with operators}, which are determined by an identity whose each term is a{ıt sum or a sum of products of sets of the form $\chi_{a}(T)$ and $\chi_{f(x)}(T)$}where $f$ maps $U^{+}$ to itself, and $\chi$ is any of the symbols $s$, $s^{0}$, or $s^{(c)}$. We solve the equation $\chi_{x}(\Delta )=\chi_{b}$ where $\chi$ is any of the symbols $s$, $s^{0}$,or $s^{(c)}$ and determine the solutions of (SSE) with operatorsof the form $(\chi_{a}\ast\chi_{x}+\chi_{b})(\Delta)=\chi_{\eta}$ and $[\chi_{a}\ast(\chi_{x})^{2}+\chi_{b}\ast\chi_{x}](\Delta)=\chi_{\eta}$and $\chi_{a}+\chi_{x}(\Delta)=\chi_{x}$ where $\chi$ isany of the symbols $s$, or $s^{0}$.