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

Shehzad U., Batul S., Sagheer D., Hussain A.

Journal of Mathematics, vol.2024, no.1, 2024 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 2024 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1155/2024/3933864
  • Journal Name: Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: double-controlled metric space (DCMS), fixed point (FP), Θ-Fuzzy almost generalized double-controlled contraction mapping (Θ-FAGDCCM), Θ-fuzzy double-controlled contraction mapping (Θ-FDCCM)
  • Uşak University Affiliated: No

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.