Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces. (26th February 2014) - Abbas, Mujahid; Ali, Basit; Romaguera, Salvador
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.