Geometric inequalities in real Banach spaces with applications

In this paper, new geometric inequalities are established in real Banach spaces. As an application, a new iterative algorithm is proposed for approximating a solution of a split equality fixed point problem (SEFPP) for a quasi-ϕ-nonexpansive semigroup. It is proved that the sequence generated by the...

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Bibliographic Details
Published in:Carpathian Journal of Mathematics 2023-01, Vol.39 (1), p.109-124
Main Author: Chidume, C. E.
Format: Article
Language:English
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In memoriam Professor Charles E. Chidume (1947- 2021)
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Summary:In this paper, new geometric inequalities are established in real Banach spaces. As an application, a new iterative algorithm is proposed for approximating a solution of a split equality fixed point problem (SEFPP) for a quasi-ϕ-nonexpansive semigroup. It is proved that the sequence generated by the algorithm converges strongly to a solution of the SEFPP in p-uniformly convex and uniformly smooth real Banach spaces, p > 1. Furthermore, the theorem proved is applied to approximate a solution of a variational inequality problem. All the theorems proved are applicable, in particular, in Lp , lp and the Sobolev spaces, W p m ( Ω ) , for p such that 2 < p p ∞.
ISSN:1584-2851
1843-4401
DOI:10.37193/CJM.2023.01.07