Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces. (26th February 2014)

• Record Type: Journal Article
• Authors: Abbas, Mujahid; Ali, Basit; Romaguera, Salvador
• Other Names: Du Wei-Shih Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-02-26
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/391952
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Wardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalized F -contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces. Some theorems on invariant approximations in normed linear spaces are also deduced. Our results extend, unify, and generalize comparable results in the literature.