Kannan nonexpansive maps on generalized Cesàro backward difference sequence space of non-absolute type with applications to summable equations

Abstract

In this article, we investigate the notion of the pre-quasi norm on a generalized Cesàro backward difference sequence space of non-absolute type (Ξ (Δ , r)) ψ under definite function ψ. We introduce the sufficient set-up on it to form a pre-quasi Banach and a closed special space of sequences (sss), the actuality of a fixed point of a Kannan pre-quasi norm contraction mapping on (Ξ (Δ , r)) ψ, it supports the property (R) and has the pre-quasi normal structure property. The existence of a fixed point of the Kannan pre-quasi norm nonexpansive mapping on (Ξ (Δ , r)) ψ and the Kannan pre-quasi norm contraction mapping in the pre-quasi Banach operator ideal constructed by (Ξ (Δ , r)) ψ and s-numbers has been determined. Finally, we support our results by some applications to the existence of solutions of summable equations and illustrative examples.