Partial hemi-metric spaces and fixed point theorems

Abstract

Inspired by Matthews’ theory of partial metric spaces and the recently introduced hemi-metric spaces of Ozturk and Radenović, we introduce the notion of partial hemi-metric spaces as a new class of generalized distance spaces. Several fundamental properties of these spaces are investigated, including convergence, Cauchy sequences, and completeness. We further establish Banach-type fixed point theorems for contraction mappings in complete partial hemi-metric spaces and provide illustrative examples supporting the obtained results. As an application, the existence and uniqueness of solutions for a nonlinear integral equation are derived within the proposed framework. The results presented here extend and unify various known fixed point theorems from metric, partial metric, and hemi-metric settings.