FIXED POINT THEOREMS FOR NONLINEAR MAPPINGS IN MODULAR METRIC SPACES

Abstract

This research presents fixed point results for a certain group of nonlinear mappings that were established on the basis of modular metric spaces. Modular metric spaces differ from classical metric spaces, hence they provide a more extensive and flexible setting for the analysis of iterative processes' convergence and stability. Not presupposing the continuity of the mappings, we manage to assert the existence and uniqueness of fixed points by means of contractive-type inequalities that have been expressed through modular functions as a result of the applications of the contractive conditions. The analysis of the convergence of sequences that are generated iteratively by these mappings has been conducted and the conditions offered have been shown to ensure strong convergence to the fixed point. Theorems which are frequently cited and known to arise in the context of metric and normed spaces are several that this paper has extended and generalized by placing them in the modular setting. To illustrate the theoretical results and to show the advantages of modular metric spaces in dealing with nonlinear problems, several examples have been provided. The results achieved have made a contribution to the fixed point theory development in generalized spaces and could be beneficial in nonlinear analysis and related applications