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Novel Θ-Fuzzy-Contraction Mappings and Existence of Solution of Nonlinear Differential Equations

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  • Usman Shehzad
  • Samina Batul
  • Dur-e-Shehwar Sagheer
  • Azhar Hussain
  • Ömer KiÅŸi

Abstract

This study pioneers the introduction of two novel concepts in the realm of double-controlled metric spaces: the Θ-fuzzy double-controlled contraction mapping and the Θ-fuzzy almost generalized double-controlled contraction mapping. These concepts represent a significant expansion of the existing framework of generalized contractions. This research establishes the existence and uniqueness of fixed points for each of these contraction mappings and provides exemplary illustrations to clarify the results. Moreover, we demonstrate the practical applicability of our findings by showing the existence of a solution to a nonlinear differential equation. The established theorems also yield various corollaries, which confirm that our results generalize and extend previously established findings in the field.

Suggested Citation

  • Usman Shehzad & Samina Batul & Dur-e-Shehwar Sagheer & Azhar Hussain & Ömer KiÅŸi, 2024. "Novel Θ-Fuzzy-Contraction Mappings and Existence of Solution of Nonlinear Differential Equations," Journal of Mathematics, Hindawi, vol. 2024, pages 1-21, December.
    • Handle: RePEc:hin:jjmath:3933864
    DOI: 10.1155/2024/3933864
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