Fixed Point Theorems in M-distance Spaces
Functional Analysis
2021-03-26 v1
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 -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 -spaces.
Cite
@article{arxiv.2103.13914,
title = {Fixed Point Theorems in M-distance Spaces},
author = {Vladyslav Babenko and Vira Babenko and Oleg Kovalenko},
journal= {arXiv preprint arXiv:2103.13914},
year = {2021}
}