Fixed point theorem for three pairs of mappings in parametric metric space
*Ria SharmaCorresponding authorria@baddiuniv.ac.inDepartment of MathematicsSchool of SciencesBaddi University of Emerging Sciences & TechnologyBaddi, Himachal Pradesh, 173205, IndiaView full profile → , Surjeet Singh Chauhan (Gonder)surjeetschauhan@yahoo.comDepartment of MathematicsUniversity Institute of Sciences (UIS)Chandigarh UniversityMohali, Punjab, 140413, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Feb 2026
- Published Online:
- 27 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2636
- Pages:
- 1–9
Abstract
Fixed point results are used in program verification, semantics of programming languages and recursive function theory, where multiple mappings may represent different processes or transformations. We established a common fixed-point theorem in Parametric metric space, utilizing weakly compatible mappings and implicit relations. By moving to Parametric Metric spaces, it covers cases where the distance function is Dynamic, which is not addressed in classical settings. These findings generalizes and enhances the existing common fixed point theorems based on the implicit relation. The use of implicit relations generalizes traditional contractive conditions, encompassing a wider range of possible inequalities and making the theorem applicable to diverse settings.
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References
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