Approximating a common fixed point of a finite family of nonlinear mappings in modular function spaces

In this study, it is our purpose to investigate an algorithm for approximating a common fixed point of a finite family of ρ-quasi-nonexpansive mappings. In addition, we propose and analyze a scheme which estimates a common fixed point of a finite family of multivalued mappings in modular function spaces. As a consequence, we establish the ρ-convergence of the proposed algorithms under some mild conditions. In addition, some numerical examples which support our main results are presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.