On fixed point results in metric spaces for large triangle-perimeter contractions
Dynamical Systems
2026-05-14 v1
Abstract
In this paper we introduce a corrected extension of Burton's theory of large contractions in the context of triangle-perimeter contractions introduced by Petrov. Combining these two lines of research, we prove a fixed point result for large triangle-perimeter contractions with an auxiliary assumption, which is of utmost importance. Firstly, we give a counterexample to the main result related to large triangle-perimeter contractions that currently exists in literature. Then, we prove that given an additional condition, a fixed point result for large triangle-perimeter contractions holds. Lastly, we illustrate with an example that this new framework is strictly broader than Burton's and Petrov's theory.
Cite
@article{arxiv.2605.13147,
title = {On fixed point results in metric spaces for large triangle-perimeter contractions},
author = {Ovidiu Popescu},
journal= {arXiv preprint arXiv:2605.13147},
year = {2026}
}