Kannan nonexpansive maps on generalized Cesàro backward difference sequence space of non-absolute type with applications to summable equations
| Autor: | Om Kalthum S. K. Mohamed, Awad A. Bakery |
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| Rok vydání: | 2021 |
| Předmět: |
Property (R)
Applied Mathematics 010102 general mathematics Structure (category theory) Cesàro sequence space Kannan contraction mapping Function (mathematics) Pre-quasi norm Fixed point Type (model theory) Space (mathematics) 01 natural sciences Sequence space 010101 applied mathematics Combinatorics Norm (mathematics) Operator ideal QA1-939 Discrete Mathematics and Combinatorics Contraction mapping Kannan nonexpansive mapping 0101 mathematics Mathematics Analysis |
| Zdroj: | Journal of Inequalities and Applications, Vol 2021, Iss 1, Pp 1-32 (2021) |
| ISSN: | 1029-242X |
| DOI: | 10.1186/s13660-021-02631-w |
| Popis: | In this article, we investigate the notion of the pre-quasi norm on a generalized Cesàro backward difference sequence space of non-absolute type $(\Xi (\Delta,r) )_{\psi }$ ( 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 $(\Xi (\Delta,r) )_{\psi }$ ( 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 $(\Xi (\Delta,r) )_{\psi }$ ( Ξ ( Δ , r ) ) ψ and the Kannan pre-quasi norm contraction mapping in the pre-quasi Banach operator ideal constructed by $(\Xi (\Delta,r) )_{\psi }$ ( 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. |
| Databáze: | OpenAIRE |
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