Fixed Point Theorems for convex contraction mappings on Partially E-Cone Metric Spaces

Abstract

In this paper, we investigate fixed point theorems for convex contraction mappings defined on partially E-cone metric spaces, a structure that extends classical cone metric spaces by incorporating a partial ordering induced by a subcone E. We establish sufficient conditions under which convex contraction mappings admit unique fixed points in this framework. Our results generalize and unify several existing fixed-point theorems in cone metric and ordered metric spaces. Illustrative examples are provided to demonstrate the applicability of our results. The study shows that partially E-cone metric spaces offer a flexible setting for analysing nonlinear mappings that may not satisfy standard contraction assumptions.