Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 12 min ago
PreprintCC BY 4.0arXiv

Common Fixed Points of Co-Cyclic and Sub-Cyclic Mappings in Complete Metric Spaces

  • Dev Raj Joshi
  • Sanjay Mishra
  • Piyush Kumar Tripathi
Open at sourcePDFDOICite

Abstract

In this paper, we introduce two new classes of cyclic-type mappings, namely, co-cyclic mappings and sub-cyclic mappings, defined on the union of two subsets of a metric space. Under suitable Jungck-type contractive conditions and compatibility assumptions, we establish unique common fixed point theorems for these mappings in complete metric spaces. The proofs are based on the construction of appropriate sequences, the associated contractive conditions, and the completeness of the underlying metric space. Examples are provided to illustrate the proposed concepts and to demonstrate the applicability of the main results. Finally, some open questions and possible directions for further research concerning co-cyclic and sub-cyclic mappings are presented.

Related

  1. Alternating Points of Set-Valued Mappings in Strong Partial b-Metric Spaces with Applications to Economic and Linguistic Adjustment
    Atanas Ilchev, Vanya Ivanova, Rumen Marinov +3
    AxiomsPeer-reviewedCC BY 4.0Geometry & topologyCrossref
  2. Differentiability of Lipschitz mappings into metric spaces: area and co-area formulas
    Behnam Esmayli, Paweł Goldstein, Piotr Hajłasz
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsGeometry & topologyarXiv
  3. Existence and Approximation of Fixed Points for a Novel Class of Mappings with Applications
    Rida Zainab, Mujahid Abbas, Muhammad Waseem Asghar
    AxiomsPeer-reviewedCC BY 4.0Geometry & topologyCrossref
  4. Fixed points for uniformly asymptotically Hölder-Lipschitz mappings
    Luciano G. Josino, Carlos Sérgio R. da Silva
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Four point analogue of Ciric-Reich-Rus type mappings with non-unique fixed points
    Irfan Ahmed, Shallu Sharma, Sahil Billawria
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{joshi2026common,
  title = {{Common Fixed Points of Co-Cyclic and Sub-Cyclic Mappings in Complete Metric Spaces}},
  author = {Dev Raj Joshi and Sanjay Mishra and Piyush Kumar Tripathi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12492},
  eprint = {2609.12492},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12492},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Common Fixed Points of Co-Cyclic and Sub-Cyclic Mappings in Complete Metric Spaces
AU  - Dev Raj Joshi
AU  - Sanjay Mishra
AU  - Piyush Kumar Tripathi
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12492
UR  - https://arxiv.org/abs/2609.12492
AB  - In this paper, we introduce two new classes of cyclic-type mappings, namely, co-cyclic mappings and sub-cyclic mappings, defined on the union of two subsets of a metric space. Under suitable Jungck-type contractive conditions and compatibility assumptions, we establish unique common fixed point theorems for these mappings in complete metric spaces. The proofs are based on the construction of appropriate sequences, the associated contractive conditions, and the completeness of the underlying metric space. Examples are provided to illustrate the proposed concepts and to demonstrate the applicability of the main results. Finally, some open questions and possible directions for further research concerning co-cyclic and sub-cyclic mappings are presented.
ER  -