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<p>This paper introduces and explores the concept of fuzzy <i>ϕ</i>-contraction to establish the existence of <i>n</i>-tupled coincidence points in partially ordered <i>GV</i>-fuzzy metric spaces. Using the unique properties of the <i>H</i>-type triangular norm, we integrate this norm into <i>GV</i>-fuzzy metric spaces. The mappings under consideration exhibit the mixed monotone property with respect to partial ordering. Furthermore, we employ the mixed <i>g</i>-monotone property of mappings to analyze their behavior within the given framework. To validate our theoretical findings, we present an illustrative example, which demonstrates the higher-dimensional analysis of the <i>ϕ</i>-contraction principle used in our primary results. As an application, we investigate the existence of solutions for a system of second-kind Fredholm nonlinear integral equations. Employing the developed fixed-point results, we establish sufficient conditions that guarantee the solvability of such integral equations within the <i>GV</i>-fuzzy metric space setting.</p>

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Multidimensional fuzzy ϕ-contraction inequality and its application

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年6月23日

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  • Uma Devi Patel,
  • Vineeta Chandra,
  • Abdelhamid Moussaoui,
  • Stojan Radenović

摘要

This paper introduces and explores the concept of fuzzy ϕ-contraction to establish the existence of n-tupled coincidence points in partially ordered GV-fuzzy metric spaces. Using the unique properties of the H-type triangular norm, we integrate this norm into GV-fuzzy metric spaces. The mappings under consideration exhibit the mixed monotone property with respect to partial ordering. Furthermore, we employ the mixed g-monotone property of mappings to analyze their behavior within the given framework. To validate our theoretical findings, we present an illustrative example, which demonstrates the higher-dimensional analysis of the ϕ-contraction principle used in our primary results. As an application, we investigate the existence of solutions for a system of second-kind Fredholm nonlinear integral equations. Employing the developed fixed-point results, we establish sufficient conditions that guarantee the solvability of such integral equations within the GV-fuzzy metric space setting.