Best Proximity Points of MT-Cyclic Contractions with Property UC. (18th May 2020)

• Record Type: Journal Article
• Authors: Aydi, Hassen; Lakzian, Hosein; Mitrović, Zoran D.; Radenović, Stojan
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 7(2020)
• Page Start: 871
• Page End: 882
• Publication Date: 2020-05-18
• Subjects: Best proximity point -- cyclic map -- MT-cyclic orbital contraction -- property UC; 46T99 -- 47T10 -- 54H25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1708390
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We initiate the notion of generalized M T - cyclic contraction mappings with respect to an auxiliary function φ and investigate the existence of a best proximity point of such mappings in the setting of metric spaces. We also prove the uniqueness of a fixed point, when we assume an additional condition, named as: property UC. Moreover, we discuss the existence and uniqueness of a fixed point of M T -cyclic orbital contractions in the context of ( b -metric) metric spaces.