A novel approach of digital parametric metric space

Dinesh, K.; Sila, Eriola; Zoto, Kastriot; Shoba, B.; Rizk, Doaa

doi:10.47974/JIM-2313

Open Access Research Article

A novel approach of digital parametric metric space

^*K. DineshCorresponding authordinesh.skksv93@gmail.comDepartment of MathematicsK. Ramakrishnan College of Engineering (Autonomous)Tiruchirappalli, Tamil Nadu, 621112, IndiaView full profile → , Eriola Silaeriola.sila@unitir.edu.alDepartment of MathematicsFaculty of Natural SciencesUniversity of TiranaTirana, AlbaniaView full profile → , Kastriot Zotokzoto@uogj.edu.alDepartment of Mathematics, Informatics and PhysicsFaculty of Natural SciencesUniversity of GjirokastraGjirokastra, 6001, AlbaniaView full profile → , B. Shobashobabalasubramaniyam@gmail.comDepartment of MathematicsSt Joseph’s College of EngineeringOMR Chennai, Tamil Nadu, 600119, IndiaView full profile → , Doaa Rizkd.hussien@qu.edu.saDepartment of MathematicsCollege of ScienceQassim UniversityBuraydah, 51452, Saudi ArabiaView full profile →

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pp. 2677–2686Vol. 28Issue 7October 2025DOI: 10.47974/JIM-2313XML

Received:: 10 Dec 2024
Published Online:: 14 Oct 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2313
Pages:: 2677–2686

Abstract

This work broadens fixed point (FP) theory by introducing results within the setting of digital parametric metric spaces (DPMS). Motivated by the discrete nature of digital data and the flexibility offered by parametric distance measures, we treat a DPMS as a structure in which separation between points is evaluated through a digitally defined metric that depends on a positive parameter. Several new FP results are established aimed at self-mappings on such spaces, and their applicability is illustrated in contexts such as computational geometry, discrete dynamical systems, and digital image analysis. The convergence patterns of iteratively generated sequences are explored under suitable contractive conditions, supporting the theoretical developments. In addition to enriching the theory of fixed points in discrete spaces, these results create potential avenues for use in problems requiring digital computation and structured data processing.

Keywords

Digital parametric metric space Fixed point Completeness Convergence Cauchy sequence

Subject Classifications

47H1055M20

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