Fixed Point Theorems in M-distance Spaces

2021/03/25 by Babenko, Vladyslav, Babenko, Vira, Kovalenko, Oleg
#47H09 #47H10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2103.13914

Abstract

We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including metric and uniform spaces. On the other hand, compared to the so-called cone metric spaces and K-metric spaces, we do not require that the distance function range has a linear structure. We also consider several applications of the obtained fixed point theorems. In particular, we consider the questions of the existence of solutions of the Fredholm integral equation in L-spaces.

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• Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance
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