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<p>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 demonstrate the applicability of our main result by finding a solution for fractional differential equation under some suitable assumptions.</p>

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

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Md Hasanuzzaman,
  • Abhishikta Das,
  • Sumit Som

摘要

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 demonstrate the applicability of our main result by finding a solution for fractional differential equation under some suitable assumptions.