# Mix-point property in quasi-pseudometric spaces

## TL;DR

This paper introduces new results on startpoint theory in bicomplete quasi-pseudometric spaces, characterizing the existence of startpoints and endpoints via the mix-point property, extending previous findings in the field.

## Contribution

It provides novel characterizations and existence results for startpoints and endpoints in quasi-pseudometric spaces using the mix-point property.

## Key findings

- Existence of startpoints and endpoints under certain conditions
- Characterization of startpoints and endpoints via mix-point property
- Extension of known results in quasi-pseudometric space theory

## Abstract

In this article, we give new results in the startpoint theory for quasi-pseudometric spaces. The results we present provide us with the existence of startpoint (endpoint, fixed point) for multi-valued maps defined on a bicomplete quasi-pseudometric space. We characterise the existence of startpoint and endpoint by the so-called \textit{mix-point property}. The present results extend known ones in the area.