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<p>In this study, we explore some of the best proximity point results for generalized proximal contractions in the setting of double-controlled metric-type spaces. A non-trivial example is given to elucidate our analysis, and some novel results are derived. The discovered results generalize previously known results in the context of a double controlled metric type space environment. This article’s proximity point results are the first of their kind in the realm of controlled metric spaces. To build on the results achieved in this article, we present an application demonstrating the usability of the given results.</p>

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Controlled proximal contractions with an application to a class of integral equations

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Mudasir Younis,
  • Haroon Ahmad

摘要

In this study, we explore some of the best proximity point results for generalized proximal contractions in the setting of double-controlled metric-type spaces. A non-trivial example is given to elucidate our analysis, and some novel results are derived. The discovered results generalize previously known results in the context of a double controlled metric type space environment. This article’s proximity point results are the first of their kind in the realm of controlled metric spaces. To build on the results achieved in this article, we present an application demonstrating the usability of the given results.