Open Access Research

Banach operator pairs and common fixed points in modular function spaces

N Hussain1, MA Khamsi2 and A Latif1*

Author Affiliations

1 Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

2 Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA

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Fixed Point Theory and Applications 2011, 2011:75  doi:10.1186/1687-1812-2011-75

Published: 3 November 2011

Abstract

In this article, we introduce the concept of a Banach operator pair in the setting of modular function spaces. We prove some common fixed point results for such type of operators satisfying a more general condition of nonexpansiveness. We also establish a version of the well-known De Marr's theorem for an arbitrary family of symmetric Banach operator pairs in modular function spaces without Δ2-condition.

MSC(2000)

primary 06F30; 47H09; secondary 46B20; 47E10; 47H10.

Keywords:
Banach operator pair; fixed point; modular function space; nearest point projection; asymptotically pointwise ρ-nonexpansive mapping