On Extended Versions of Dancs- Heged\"us-Medvegyev's Fixed Point Theorem

TL;DR

This paper extends fixed point theorems in quasi-metric spaces, unifying and improving upon several previous results, with illustrative examples demonstrating the significance of these advancements.

Contribution

It introduces new fixed point theorems in quasi-metric spaces that generalize and strengthen prior results from multiple researchers.

Findings

Unified fixed point theorems in quasi-metric spaces

Extensions of Dancs-Hegedüs-Medvegyev's theorem

Illustrative examples showing improvements

Abstract

In this article we establish some fixed point (known also as critical point, invariant point) theorems in quasi-metric spaces. Our results unify and further extend in some regards the fixed point theorem proposed by Dancs et al. (1983), the results given by Khanh and Quy (2010, 2011), the preorder principles established by Qiu (2014), and the results obtained by Bao et al. (2015). In addition, we provide examples to illustrate that the improvements of our results are significant.