[PDF] Top 20 Weak and strong convergence theorems of implicit iteration process on Banach spaces

... Let E be a Banach space, and let C be a nonempty closed convex subset of E. A map- ping T: C ® E is nonexpansive if ||Tx - Ty|| ≤ ||x - y|| for every x, y Î C. Let F(T): = {x Î C: x = Tx} denote the set of fixed ... See full document

... several weak and strong convergence theorems are established for a new modified iteration with errors for a finite family of nonself mappings which are asymptotically nonexpansive in the ... See full document

... We first introduce an iterative sequence for finding fixed points of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by ... See full document

... In this paper, without other specifications, let R be the set of real numbers, C be a nonempty, closed and convex subset of a real reflexive Banach space E with the dual space E ∗ . The norm and the dual pair ... See full document

... following strong convergence ...convex Banach space, let K be a nonempty closed convex subset of E, let T : K → K be a nonexpansive mapping with nonempty fixed points set F, and let T be ... See full document

... Lemma 3.1. Let C be a nonempty weakly compact convex subset of a Banach space E and let ᏿ = { T(t) : t ∈ S } be a nonexpansive semigroup on C such that F( ᏿ ) = ∅ . Let X be a subspace of B(S) with 1 ∈ X such that ... See full document

... Some weak and strong convergence theorems for monotone Lipschitzian mappings were established by several authors 7, ...Therefore, Theorems 5.7 and 5.8 provide a new convergence ... See full document

... Let D be a nonempty closed convex subset of a real Banach space X. A single-valued mapping T : D ® D is called nonexpansive if ||T(x) - T(y)|| ≤ ||x - y|| for all x, y Î D. Let N(D) and CB(D) denote the family of ... See full document

... the implicit iteration process (.) and to prove some strong and weak convergence theorems for a continuous pseudocontractive map- ping and a weak ... See full document

... the implicit iteration introduced by Xu and Ori 5 for a finite family of nonexpansive mappings in a Hilbert space, Osilike 6, Chen et ...studied convergence theorems for an implicit ... See full document

... Bregman weak relatively nonexpansive mapping for each i = , , ...some strong convergence theorems for these ...reflexive Banach space ... See full document

... introduced implicit iteration process to approximate a common fixed point of a finite family of nonexpansive mappings in a Hilbert ...an implicit iteration process for a finite ... See full document

... proved strong convergence result of Mann iteration for I-nonexpansive ...weakly convergence result for asymptotically I-nonexpansive mapping in Hilbert ...[8] weak and strong ... See full document

... an implicit predictor-corrector iteration process for finitely many asymptoti- cally quasi-nonexpansive self-mappings on a nonempty closed convex subset of a Banach space ...the strong ... See full document

... 26 Y. I. Alber, “Metric and generalized projection operators in Banach spaces: properties and applications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, A. G. ... See full document

... Zembayashi, “Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications [r] ... See full document

... proved weak and strong convergence theorems of this iteration process for finding common fixed points of two G-nonexpansive mappings in a uniformly convex Banach ... See full document

... general implicit iterative algorithm, which includes an explicit process as a special ..., weak convergence theorems are established in a uniformly convex Banach ... See full document

... proved strong convergence and weak convergence theorems with the help of his process for the class of nonexpansive mappings in general Banach spaces and apply it to ... See full document

... The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and ... See full document