On monotone mappings in modular function spaces


Buthinah A. Bin Dehaish - Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21593, Saudi Arabia. Mohamed A. Khamsi - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.


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 Göhde 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.