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

Fixexd point theory and applications

Mohamed Amine Khamsi¹  Abdullah Al-Roqi²  Saleh Abdullah Al-Mezel² 

[1] Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, USA;Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: convexity structure;    fixed point;    modular function space;    nonexpansive mappings;    normal structure;    retract;   

DOI  :  10.1186/1687-1812-2012-109

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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 ρ-nonexpansive mappings defined on a nonempty, ρ-closed and ρ-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.

【 授权许可】

CC BY