Abstract
We prove the existence of fixed points of monotone rho-nonexpansive mappings in rho-uniformly convex modular function spaces. This is the modular version of Browder and Gohde fixed point theorems for monotone mappings. We also discuss the validity of this result in modular function spaces where the modular is uniformly convex in every direction. This property has never been considered in the context of modular spaces. (C)2016 All rights reserved.