Banach operator pairs and common fixed points in modular function spaces
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
Fixed Point Theory and Applications 2011, 2011:75 doi:10.1186/1687-1812-2011-75Published: 3 November 2011
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.
primary 06F30; 47H09; secondary 46B20; 47E10; 47H10.