Kannan nonexpansive maps on generalized Ces\xe0ro backward difference sequence space of non-absolute type with applications to summable equations

Awad A Bakery,Om Kalthum S K Mohamed

doi:10.1186/s13660-021-02631-w

Awad A Bakery, Om Kalthum S K Mohamed

Open Access

https://doi.org/10.1186/s13660-021-02631-w

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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 (Xi (Delta,r) )_{psi } 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 (Xi (Delta,r) )_{psi }, 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 (Xi (Delta,r) )_{psi } and the Kannan pre-quasi norm contraction mapping in the pre-quasi Banach operator ideal constructed by (Xi (Delta,r) )_{psi } 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.

Highlights

Ideal operator theorems are very important in mathematical models and have numerous implementations, such as normal series theory, ideal transformations, geometry of Banach spaces, approximation theory, fixed point theory, and so forth
3 The sequence space ( (, r))ψ We introduce the definition of generalized Cesàro backward difference sequence space of non-absolute type ( (, r))ψ under the function ψ and some inclusion relations
4 Pre-quasi norm on (, r) We investigate the sufficient set-up on (, r) with a pre-quasi norm ψ to form a pre-quasi Banach and a closed

Summary

Introduction

Ideal operator theorems are very important in mathematical models and have numerous implementations, such as normal series theory, ideal transformations, geometry of Banach spaces, approximation theory, fixed point theory, and so forth. The point g ∈ ( ( , r))ψ is the only fixed point of W if the following conditions are satisfied: (a) W is a Kannan ψ-contraction mapping; (b) W is ψ -sequentially continuous at a point g ∈ ( ( , r))ψ ; (c) There is v ∈ ( ( , r))ψ so that the sequence of iterates {W pv} has a subsequence

Results

Conclusion