Best Proximity Point Results for Contractive and Cyclic Contractive Type Mappings. (1st July 2021)

• Record Type: Journal Article
• Authors: Hiranmoy, Garai; Karapınar, Erdal; Kanta Dey, Lakshmi
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 7(2021)
• Page Start: 849
• Page End: 864
• Publication Date: 2021-07-01
• Subjects: Best proximity point -- compact weakly proximal pair -- cyclic mapping -- Proximal Chatterjea type contractive mapping -- Proximal Kannan type contractive mapping; 47H10 -- 54H25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1933518
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The essential importance of the best proximity point theory is that "best proximity point theory" appears in the coincidence of "metric fixed point theory" and "optimization theory." So finding best proximity points of mappings satisfying different type of contractive conditions in different structures is one of the fascinating research topics. For this, in this article, we first introduce a new type of proximal property of a pair of subsets of a metric space, which we designate as proximal weakly compact pair. After this, we come up with some new type of proximal contractive and proximal cyclic contractive mappings. Then we investigate the existence of best proximity point(s) in these newly originated mappings in the setting of proximal weakly compact pair of subsets in a metric space.