Three point analogue of Ćirić-Reich-Rus type mappings with non-unique fixed points
arXiv:2502.02595 · doi:10.1007/s41478-024-00743-2
Abstract
In this paper, we introduce a three-point analogue of Ćirić-Reich-Rus type mappings, termed as generalized Ćirić-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 Ćirić-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 Ćirić-Reich-Rus type mappings in metric spaces that are not necessarily complete.
19 pages. arXiv admin note: substantial text overlap with arXiv:2403.07906; text overlap with arXiv:2308.05419