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

Md Hasanuzzaman; Abhishikta Das; Sumit Som

doi:10.1007/s40995-026-02013-1

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arXiv · 2509.10497

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

Md Hasanuzzaman·Abhishikta Das·Sumit Som

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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.

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Md Hasanuzzaman, Abhishikta Das, Sumit Som. 2025-08-31. Relation-Theoretic Banach Contraction Principle in Topological Spaces with an Application. https://doi.org/10.1007/s40995-026-02013-1

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