Fixed Point Theorems for Hardy--Rogers Type Multivalued Mappings in b-Metric Spaces
Abstract
In this paper, we establish new fixed point theorems for multivalued mappings satisfying Hardy-Rogers type contractive conditions in complete b-metric spaces. Motivated by the constant-coefficient framework of Chaib et al. (Fixed Point Theory 27 (2026), 209-228), we develop a distance-dependent formulation in which the contractive coefficients are nonnegative functions of the interpoint distance. We introduce a piecewise contraction factor corresponding to the two cases determined by the relative sizes of the cross terms in the Hardy-Rogers inequality, thereby providing a formulation adapted to the structure of the contractive condition. Under appropriate assumptions on the coefficient functions, we establish fixed point existence through either h-upper semicontinuity or asymptotic limsup conditions. The resulting framework yields corresponding fixed point theorems for multivalued Reich, Kannan, and Chatterjea-type contractions. We further investigate strict fixed points and obtain conditions under which the fixed point and strict fixed point sets coincide and consist of a unique point. In addition, we establish a fixed point transfer result for suitable finite iterates, showing that the contractive condition may be imposed on Tp rather than on the original mapping, provided that the latter has a strict fixed point. Corresponding single-valued consequences are also derived. Several examples illustrate the applicability of the results and demonstrate situations in which the proposed conditions apply beyond the corresponding existing formulations.
Related
- Fixed Point Theorems for Paired Contractive Mappings in b-Metric Spaces
- Hardy–Rogers-Type Fixed-Point and Fixed-Disc Results on Quasi M-Metric Spaces
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- Differentiability of Lipschitz mappings into metric spaces: area and co-area formulas
- Common Fixed Points of Co-Cyclic and Sub-Cyclic Mappings in Complete Metric Spaces
BibTeX
@misc{adewinbi2026fixed,
title = {{Fixed Point Theorems for Hardy--Rogers Type Multivalued Mappings in b-Metric Spaces}},
author = {Hezekiah Seun Adewinbi and Oluwatosin Temitope Mewomo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.13286},
eprint = {2608.13286},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13286},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fixed Point Theorems for Hardy--Rogers Type Multivalued Mappings in b-Metric Spaces
AU - Hezekiah Seun Adewinbi
AU - Oluwatosin Temitope Mewomo
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2608.13286
UR - https://arxiv.org/abs/2608.13286
AB - In this paper, we establish new fixed point theorems for multivalued mappings satisfying Hardy-Rogers type contractive conditions in complete b-metric spaces. Motivated by the constant-coefficient framework of Chaib et al. (Fixed Point Theory 27 (2026), 209-228), we develop a distance-dependent formulation in which the contractive coefficients are nonnegative functions of the interpoint distance. We introduce a piecewise contraction factor corresponding to the two cases determined by the relative sizes of the cross terms in the Hardy-Rogers inequality, thereby providing a formulation adapted to the structure of the contractive condition. Under appropriate assumptions on the coefficient functions, we establish fixed point existence through either h-upper semicontinuity or asymptotic limsup conditions. The resulting framework yields corresponding fixed point theorems for multivalued Reich, Kannan, and Chatterjea-type contractions. We further investigate strict fixed points and obtain conditions under which the fixed point and strict fixed point sets coincide and consist of a unique point. In addition, we establish a fixed point transfer result for suitable finite iterates, showing that the contractive condition may be imposed on T^p rather than on the original mapping, provided that the latter has a strict fixed point. Corresponding single-valued consequences are also derived. Several examples illustrate the applicability of the results and demonstrate situations in which the proposed conditions apply beyond the corresponding existing formulations.
ER -