On generalizations of some fixed point theorems in semimetric spaces with triangle functions
Abstract
In the present paper, we prove generalizations of Banach, Kannan, Chatterjea, \'Ciri\'c-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mappings contracting perimeters of triangles. We consider corresponding mappings in semimetric spaces with triangle functions introduced by M. Bessenyei and Z. P\'ales. Such an approach allows us to derive corollaries for various types of semimetric spaces including metric spaces, ultrametric spaces, b-metric spaces etc. The significance of these generalized theorems extends across multiple disciplines, including optimization, mathematical modeling, and computer science. They may serve to establish stability conditions, demonstrate the existence of optimal solutions, and improve algorithm design.
Cite
@article{arxiv.2501.04723,
title = {On generalizations of some fixed point theorems in semimetric spaces with triangle functions},
author = {Evgeniy Petrov and Ruslan Salimov and Ravindra K. Bisht},
journal= {arXiv preprint arXiv:2501.04723},
year = {2025}
}
Comments
17 pages, This is the submitted version. The published version is available at https://doi.org/10.3389/fams.2024.1392560. arXiv admin note: substantial text overlap with arXiv:2501.00392