The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings. (29th August 2013)

• Record Type: Journal Article
• Authors: Sintunavarat, Wutiphol; Kumam, Poom
• Other Names: Vetro Calogero Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-08-29
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/375604
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Recently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contractions of the first and second kinds which are more general than the notion of self-contractions, establish the existence of an optimal approximate solution theorems for these non-self-mappings, and also give examples to validate our main results.