FIXED POINTS OF ENRICHED ρ-NONEXPANSIVE MAPPINGS IN MODULAR FUNCTION SPACES

In this paper, we initiate the study of enriched ρ-nonexpansive mappings in modular function spaces. First we show that in modular function spaces, every ρ-nonexpansive mapping is enriched ρ-nonexpansive mapping but not conversely and that their sets of fixed point are same. Next, we prove a ρ-convergence result on approximation of fixed points of enriched ρ-nonexpansive mappings in modular function spaces. We verify the validity of the result by an example. We construct a table to show our findings. Finally, we give one more ρ-convergence result under different conditions. Our results are new for ρ-nonexpansive mappings in modular function spaces.