Best Proximity Points for Some Classes of Proximal Contractions. (29th September 2013)

• Record Type: Journal Article
• Authors: Alghamdi, Maryam A.; Shahzad, Naseer; Vetro, Francesca
• Other Names: Karapinar E. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-09-29
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/713252
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Given a self-mapping g : A → A and a non-self-mapping T : A → B, the aim of this work is to provide sufficient conditions for the existence of a unique point x ∈ A, called g -best proximity point, which satisfies d g x, T x = d A, B . In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function x → d g x, T x, thereby getting an optimal approximate solution to the equation T x = g x . An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-self-mappings.