Relation-Theoretic Banach Contraction Principle in Topological Spaces with an Application

2025/08/31 by Md Hasanuzzaman, Hasanuzzaman, Md, Abhishikta Das +3
Computer Science · #47H10 #54H25 #FOS: Mathematics #General Mathematics (math.GM) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2509.10497

openalex publication_date 2025/08/31 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

In this article, we extend several relation-theoretic notions to topological spaces. We introduce relation preserving contraction mapping into topological spaces and utilize the same to extend Banach contraction principle in topological spaces employing a binary relation. To illustrate the validity of our main result, we provide a concrete example along with a MATLAB-based visualization of the convergence behavior. Furthermore, we demonstrated the applicability of our main result by finding a solution for a fractional differential equation under some suitable assumptions.

Citations

• Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales

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