An Implicit Relation Approach in Metric Spaces under w-Distance and Application to Fractional Differential Equation. (7th June 2021)

• Record Type: Journal Article
• Authors: Jain, Reena; Nashine, Hemant Kumar; Kumar, Santosh
• Other Names: Vetro Calogero Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-06-07
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/9928881
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : The purpose of this work is to introduce a new class of implicit relation and implicit type contractive condition in metric spaces under w -distance functional. Further, we derive fixed point results under a new class of contractive condition followed by three suitable examples. Next, we discuss results about weak well-posed property, weak limit shadowing property, and generalized w -Ulam-Hyers stability of the mappings of a given type. Finally, we obtain sufficient conditions for the existence of solutions for fractional differential equations as an application of the main result.