Caristi's Fixed Point Theorem in Cone Metric Space. (17th March 2022)

• Record Type: Journal Article
• Authors: Lael, Fatemeh; Saleem, Naeem; George, Reny
• Other Names: Avery Richard I. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-03-17
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/7523333
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we provide a short, comprehensive, and brief proof for Caristi-Kirk fixed point result for single and set-valued mappings in cone metric spaces. In addition, we partially addressed an open problem in which Caristi-Kirk fixed point result in cone metric spaces reduces to a classical result in metric spaces and provided a brief justification for a partial positive answer to this open problem using Caristi-Kirk fixed point theorem on uniform space. The proofs given to Caristi-Kirk's result vary and use different techniques.