Journal of Inequalities and Applications (Jun 2021)

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

  • Awad A. Bakery,
  • Om Kalthum S. K. Mohamed

DOI
https://doi.org/10.1186/s13660-021-02631-w
Journal volume & issue
Vol. 2021, no. 1
pp. 1 – 32

Abstract

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

Keywords