INEXACT ORBITS OF NONEXPANSIVE MAPPINGS

Convergence to Compact Sets of Inexact Orbits of Nonexpansive Mappings in Banach and Metric Spaces

Convergence of Inexact Iterative Schemes for Nonexpansive Set-Valued Mappings

Generalized Asymptotic Pointwise Contractions and Nonexpansive Mappings Involving Orbits

Four recent papers 1–4 present simple and elegant proofs of fixed point results for pointwise contractions, asymptotic pointwise contractions, and asymptotic nonexpansive mappings. Kirk and Xu 1 study these mappings in the context of weakly compact convex subsets of Banach spaces, respectively, in uniformly convex Banach spaces. Hussain and Khamsi 2 consider these problems in the framework of m...

On Firmly Nonexpansive Mappings

It is shown that any A-firmly, 0 < A < 1 , nonexpansive mapping T: C —> C has a fixed point in C whenever C is a finite union of nonempty, bounded, closed convex subsets of a uniformly convex Banach space. Let C be a nonempty subset of a Banach space X, and let X £ (0, 1). Then a mapping T: C —> X is said to be X-firmly nonexpansive if (1) \\Tx Ty\\ < ||(1 X)(x y)+X(Tx Ty)\\ for all x, y £ C. I...

Approximating fixed points of generalized nonexpansive mappings