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<p>In this work, we introduce the notion of asymptotically weak closed structures within an appropriate binary relation framework. Under suitable assumptions on the relational and asymptotic weak conditions, we establish existence and uniqueness of fixed points in this generalized setting. These findings extend a wide range of fixed point theorems already established in the literature. We support our findings with a nontrivial example in which previous results cannot be applied, but our approach successfully provides a solution. The theoretical findings are then applied to an exothermic chemical reactor problem, where the governing differential equation is transformed into a Hammerstein integral equation. Utilizing the developed fixed point theorems, we demonstrate the existence of a unique steady-state temperature profile of the reactor. This approach provides a rigorous mathematical foundation for analyzing nonlinear reaction-diffusion systems under physically relevant constraints.</p>

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Some fixed point results based on asymptotically weak closed structures with applications to an exothermic chemical reactor problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月19日

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  • Min Wang,
  • Muhammad Din,
  • Mi Zhou,
  • Mohammad Akram

摘要

In this work, we introduce the notion of asymptotically weak closed structures within an appropriate binary relation framework. Under suitable assumptions on the relational and asymptotic weak conditions, we establish existence and uniqueness of fixed points in this generalized setting. These findings extend a wide range of fixed point theorems already established in the literature. We support our findings with a nontrivial example in which previous results cannot be applied, but our approach successfully provides a solution. The theoretical findings are then applied to an exothermic chemical reactor problem, where the governing differential equation is transformed into a Hammerstein integral equation. Utilizing the developed fixed point theorems, we demonstrate the existence of a unique steady-state temperature profile of the reactor. This approach provides a rigorous mathematical foundation for analyzing nonlinear reaction-diffusion systems under physically relevant constraints.