Three point analogue of \'Ciri\'c-Reich-Rus type mappings with non-unique fixed points
Abstract
In this paper, we introduce a three-point analogue of \'Ciri\'c-Reich-Rus type mappings, termed as generalized \'Ciri\'c-Reich-Rus type mappings. We demonstrate that these mappings generally exhibit discontinuity within their domain of definition but necessitate continuity at their fixed points. We showcase the existence and non-uniqueness of fixed points for these generalized \'Ciri\'c-Reich-Rus type mappings. By imposing additional conditions, specifically asymptotic regularity and continuity, we extend the applicability of fixed-point theorems to a broader class of mappings. Finally, we obtain two fixed point theorems for generalized \'Ciri\'c-Reich-Rus type mappings in metric spaces that are not necessarily complete.
Keywords
Cite
@article{arxiv.2502.02595,
title = {Three point analogue of \'Ciri\'c-Reich-Rus type mappings with non-unique fixed points},
author = {Ravindra K. Bisht and Evgeniy Petrov},
journal= {arXiv preprint arXiv:2502.02595},
year = {2025}
}
Comments
19 pages. arXiv admin note: substantial text overlap with arXiv:2403.07906; text overlap with arXiv:2308.05419