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Peer-reviewedCC BY 4.0Mathematics

Hardy–Rogers-Type Fixed-Point and Fixed-Disc Results on Quasi M-Metric Spaces

  • Nihal Taş1
  • Elif Kaplan2
  • Meltem Erden Ege3
  • Mohammed Rabih4
4 affiliations
  1. 1Department of Mathematics, Balıkesir University, 10145 Balıkesir, Turkey
  2. 2Department of Mathematics, Ondokuz Mayıs University, 55200 Samsun, Turkey
  3. 3Independent Researcher, 35000 Izmir, Turkey
  4. 4Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
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Abstract

In this manuscript, we investigate original fixed-point (fp) and fixed-disc results in quasi M-metric spaces. First, we present a Hardy–Rogers-type fp result for self-mappings satisfying a specific contractive condition in mq-complete quasi M-metric spaces. Furthermore, we extend these results to an integral-type contraction, providing a more generalized version of the Hardy–Rogers fp theorem. In the second part of this study, we address the fixed-disc problem, which generalizes the fixed-circle problem to the setting of quasi M-metric spaces. We establish both forward and backward Hardy–Rogers-type fixed-disc theorems, identifying the conditions under which a self-mapping T fixes a disc Dζ0,β. The existence and uniqueness of such fps and discs are supported by detailed proofs and illustrative examples. Our results extend and unify several existing theorems in the literature, including Banach- and Kannan-type results on quasi M-metric spaces.

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Cite

BibTeXRIS
BibTeX
@article{tas2026hardyrogerstype,
  title = {{Hardy–Rogers-Type Fixed-Point and Fixed-Disc Results on Quasi M-Metric Spaces}},
  author = {Nihal Taş and Elif Kaplan and Meltem Erden Ege and Mohammed Rabih},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203754},
  url = {https://www.mdpi.com/2227-7390/14/20/3754},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Hardy–Rogers-Type Fixed-Point and Fixed-Disc Results on Quasi M-Metric Spaces
AU  - Nihal Taş
AU  - Elif Kaplan
AU  - Meltem Erden Ege
AU  - Mohammed Rabih
PY  - 2026
DA  - 2026/10/16
JO  - Mathematics
DO  - 10.3390/math14203754
UR  - https://www.mdpi.com/2227-7390/14/20/3754
AB  - In this manuscript, we investigate original fixed-point (fp) and fixed-disc results in quasi M-metric spaces. First, we present a Hardy–Rogers-type fp result for self-mappings satisfying a specific contractive condition in mq-complete quasi M-metric spaces. Furthermore, we extend these results to an integral-type contraction, providing a more generalized version of the Hardy–Rogers fp theorem. In the second part of this study, we address the fixed-disc problem, which generalizes the fixed-circle problem to the setting of quasi M-metric spaces. We establish both forward and backward Hardy–Rogers-type fixed-disc theorems, identifying the conditions under which a self-mapping T fixes a disc Dζ0,β. The existence and uniqueness of such fps and discs are supported by detailed proofs and illustrative examples. Our results extend and unify several existing theorems in the literature, including Banach- and Kannan-type results on quasi M-metric spaces.
SN  - 2227-7390
ER  -