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One-local retract and common fixed point in modular function spaces
Journal article   Open access  Peer reviewed

One-local retract and common fixed point in modular function spaces

Saleh Abdullah Al-Mezel, Abdullah Al-Roqi and Mohamed Amine Khamsi
Fixed point theory and applications (Hindawi Publishing Corporation), Vol.2012(1), pp.1-13
05/07/2012
DOI: https://doi.org/10.1186/1687-1812-2012-109

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
In this paper, we introduce and study the concept of one-local retract in modular function spaces. In particular, we prove that any commutative family of rho-nonexpansive mappings defined on a nonempty, rho-closed and rho-bounded subset of a modular function space has a common fixed point provided its convexity structure of admissible subsets is compact and normal. MSC: Primary 47H09; Secondary 46B20, 47H10.
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https://doi.org/10.1186/1687-1812-2012-109View
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