On the equivalence of the Mizoguchi-Takahashi locally contractive map to Nadler's locally contractive map

TL;DR

This paper proves the equivalence between Mizoguchi-Takahashi and Nadler's locally contractive maps in metrically convex spaces, unifying two approaches in fixed point theory.

Contribution

It establishes the equivalence of two locally contractive map concepts, enhancing understanding in fixed point theory for multi-valued maps.

Findings

Proved the equivalence of Mizoguchi-Takahashi and Nadler's maps

Unified two approaches in fixed point theory

Applicable in metrically convex spaces

Abstract

In this article, we have proved the equivalence between the Mizoguchi-Takahashi uniformly~locally~contractive map to the multi-valued map satisfying the Nadler contractive condition uniformly~locally~on a metrically convex space.