Some remarks on generalized Kirk's process in Banach spaces and application

Abstract

In this work, we establish a common fixed point result for mappings satisfying a controllable punctual inequality and we study the convergence (resp. weak convergence) of the generalized Kirk's process associated with them. In addition, our results are applied to investigate the convergence (resp. weak convergence) of Kuhfittig's iterative process to the solution of a nonlinear system of functional equations.