Best Proximity Point Results in Complex Valued Metric Spaces. (26th August 2014)

• Record Type: Journal Article
• Authors: Choudhury, Binayak S.; Metiya, Nikhilesh; Maity, Pranati
• Other Names: Hu Ying Academic Editor.
• Is Part Of: International journal of analysis. Volume 2014(2014)
• Publication Date: 2014-08-26
• Subjects: Mathematical analysis -- Periodicals; 515.05
• DOI: 10.1155/2014/827862
• Languages: English
• ISSNs: 2314-498X

Abstract

Abstract : We introduce the concept of proximity points for nonself-mappings between two subsets of a complex valued metric space which is a recently introduced extension of metric spaces obtained by allowing the metric function to assume values from the field of complex numbers. We apply this concept to obtain the minimum distance between two subsets of the complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.