Startpoints via weak contractions

TL;DR

This paper introduces new results on startpoints in quasi-pseudometric spaces using generalized weakly contractive set-valued maps, expanding the fixed point theory in these spaces.

Contribution

It provides novel theorems for startpoints in quasi-pseudometric spaces based on generalized weak contractions, advancing the fixed point theory for multi-valued maps.

Findings

New existence theorems for startpoints in quasi-pseudometric spaces

Extension of fixed point results to weakly contractive set-valued maps

Broader applicability in the study of multi-valued fixed points

Abstract

Startpoints (resp. endpoints) can be defined as "oriented fixed points". They arise naturally in the study of fixed for multi-valued maps defined on quasi-metric spaces. In this article, we give a new result in the startpoint theory for quasi-pseudometric spaces. The result we present is obtained via a generalized weakly contractive set-valued map.