On Rational Contractions and Fixed Points in m-Hemi-Metric Spaces
Abstract
In this paper, we investigate rational contraction mappings in the setting of m-hemi-metric spaces. Unlike the classical rational contractions formulated in metric, G-metric, and b-metric spaces, the proposed contractive condition is established directly within the framework of m-hemi-metrics by exploiting their multi-point distance structure. Under this nonlinear rational contractive condition, we prove an existence and uniqueness theorem for fixed points in h-complete m-hemi-metric spaces. Several examples are presented to illustrate the applicability of the proposed contraction. As an application, we establish the existence and uniqueness of continuous solutions for a class of nonlinear Fredholm integral equations by means of the obtained fixed point theorem. The results extend Banach-type fixed point theory to the setting of m-hemi-metric spaces and contribute to the study of nonlinear problems in generalized distance spaces.
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