One-local retract and common fixed point in modular function spaces
1 Department of Mathematics, King Abdulaziz University, PO Box 80203, Jeddah 21589, Saudi Arabia
2 Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA
Fixed Point Theory and Applications 2012, 2012:109 doi:10.1186/1687-1812-2012-109Published: 5 July 2012
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.