Four point analogue of Ciric-Reich-Rus type mappings with non-unique fixed points
Abstract
In this paper, we introduce and study a new class of mappings termed generalized quadrilateral Ciric-Reich-Rus type mappings, which serve as a four-point analogue of Ciric- Reich-Rus type mappings. We establish the existence and non-uniqueness of fixed points, with at most three fixed points possible for these mappings in complete metric spaces under the condition that the mapping has no periodic points of prime period 2 and 3. We determine that while these mappings are often discontinuous within their domain of definition, they must be continuous at their fixed points. By applying additional constraints, notably asymptotic regularity and continuity, we broaden the applicability of fixed-point theorems to include a broader class of mappings. At the end, we attain fixed point theorems for generalized quadrilateral Ciric- Reich-Rus type mappings in metric spaces that are not necessarily complete. Several illustrative examples are provided to validate the theoretical results and demonstrate the independence of our new class from existing notions.
Related
- Existence and Approximation of Fixed Points for a Novel Class of Mappings with Applications
- Common Fixed Points of Co-Cyclic and Sub-Cyclic Mappings in Complete Metric Spaces
- Fixed points for uniformly asymptotically Hölder-Lipschitz mappings
- Alternating Points of Set-Valued Mappings in Strong Partial b-Metric Spaces with Applications to Economic and Linguistic Adjustment
- Best proximity point results of operator type condensing mappings via measure of noncompactness and application to an infinite system of differential equations in c0 and ℓ1
BibTeX
@misc{ahmed2026four,
title = {{Four point analogue of Ciric-Reich-Rus type mappings with non-unique fixed points}},
author = {Irfan Ahmed and Shallu Sharma and Sahil Billawria},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06864},
eprint = {2610.06864},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06864},
}
RIS
TY - UNPB
TI - Four point analogue of Ciric-Reich-Rus type mappings with non-unique fixed points
AU - Irfan Ahmed
AU - Shallu Sharma
AU - Sahil Billawria
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.06864
UR - https://arxiv.org/abs/2610.06864
AB - In this paper, we introduce and study a new class of mappings termed generalized quadrilateral Ciric-Reich-Rus type mappings, which serve as a four-point analogue of Ciric- Reich-Rus type mappings. We establish the existence and non-uniqueness of fixed points, with at most three fixed points possible for these mappings in complete metric spaces under the condition that the mapping has no periodic points of prime period 2 and 3. We determine that while these mappings are often discontinuous within their domain of definition, they must be continuous at their fixed points. By applying additional constraints, notably asymptotic regularity and continuity, we broaden the applicability of fixed-point theorems to include a broader class of mappings. At the end, we attain fixed point theorems for generalized quadrilateral Ciric- Reich-Rus type mappings in metric spaces that are not necessarily complete. Several illustrative examples are provided to validate the theoretical results and demonstrate the independence of our new class from existing notions.
ER -