Ergodic Retractions for Families of Asymptotically Nonexpansive Mappings

Ergodic Retractions for Families of Asymptotically Nonexpansive Mappings

Correspondence should be addressed to Shahram Saeidi, [email protected] Received 2 October 2009; Revised 10 January 2010; Accepted 14 March 2010 Academic Editor: Mohamed Amine Khamsi Copyright q 2010 Shahram Saeidi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided t...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Convergece Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings

Let E be a real Banach space, K a closed convex nonempty subset of E, and T1,T2, . . . ,Tm : K → K asymptotically quasi-nonexpansive mappings with sequences (resp.) {kin}n=1 satisfying kin → 1 as n → ∞, and ∑∞ n=1(kin − 1) < ∞, i = 1,2, . . . ,m. Let {αn}n=1 be a sequence in [ , 1− ], ∈ (0,1). Define a sequence {xn} by x1 ∈ K , xn+1 = (1− αn)xn + αnT n 1 yn+m−2, yn+m−2 = (1− αn)xn + αnT 2 yn+m−...

Weak Convergence Theorems for Asymptotically Nonexpansive Mappings and Total Asymptotically Nonexpansive Non-Self Mappings

In this paper, we proposed a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two total asymptotically nonexpansive non-self mappings and establish some weak convergence theorems for mentioned scheme and mappings in the setting of uniformly convex Banach spaces. Our results extend and generalize several results from the current existing li...

a mean ergodic theorem for asymptotically quasi-nonexpansive affine mappings in banach spaces satisfying opial's condition