A New Approach to Fuzzy Differential Equations Using Weakly-Compatible Self-Mappings in Fuzzy Metric Spaces. (12th October 2021)

• Record Type: Journal Article
• Authors: Shamas, Iqra; Rehman, Saif Ur; Jan, Naeem; Gumaei, Abdu; Al-Rakhami, Mabrook
• Other Names: Drihem Douadi Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-10-12
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/6123154
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : The key objective of this research article includes the study of some rational type coincidence point and deriving common fixed point (CFP) results for rational type weakly-compatible three self-mappings in fuzzy metric (FM) space. The "triangular property of FM" is used as a fundamental tool. Moreover, some unique coincidence points and CFP theorems were presented for three self-mappings in an FM space under the conditions of rational type weakly-compatible fuzzy-contraction. In addition, some suitable examples are also given. Furthermore, an application of fuzzy differential equations is provided in the aid of the proposed work. Hence, the innovative direction of rational type weakly-compatible fuzzy-contraction with the application of fuzzy differential equations in FM space will certainly play a vital role in the related fields. It has the potential to be extended in any direction with different types of weakly-compatible fuzzy-contraction conditions for self-mappings with different types of differential equations.