[PDF] Top 20 An implicit iterative algorithm with errors for two families of generalized asymptotically nonexpansive mappings

... For iterative algorithms, the most oldest and simple one is Picard iterative ...Picard iterative algorithm can converge to the unique fixed ...general nonexpansive mappings, ... See full document

... [] generalized the result of Nakajo and Takahashi by proving strong con- vergence theorems for asymptotically nonexpansive mappings and asymptotically nonex- pansive ...for two ... See full document

... asymptotically nonexpansive mappings in Banach ...of two nonexpansive mappings and a finite family of nonexpansive mappings, and proved some convergence theorems for ... See full document

... an implicit iterative process with errors converges strongly to a com- mon fixed point for a finite family of generalized asymptotically quasi-nonexpansive mappings on ... See full document

... general implicit iterative process studied by Qin et ...explicit iterative processes and Sun’s implicit iterative processes as special cases for two fi- nite families of ... See full document

... of asymptotically nonexpansive map- ping, which is closely related to the theory of fixed points in Banach ...Mann iterative sequences for approximating the fixed points of a class of ... See full document

... modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically ... See full document

... of asymptotically nonexpansive mappings was in- troduced by Goebel and Kirk [4] who proved that every asymptotically nonexpansive self-mapping of nonempty closed bounded and convex ... See full document

... ϕ (y) − ϕ (x) ≥ 0, ∀ y ∈ C. (1 : 7) The above formulation (1.5) was shown in [1] to cover monotone inclusion pro- blems, saddle point problems, variational inequality problems, minimization problems, optimization ... See full document

... an implicit iterative process with errors converges weakly and strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings on unbounded sets ... See full document

... The purpose of this paper is to study the convergence of the implicit iteration process 1.18 for two finite families of generalized asymptotically quasi-nonexpansive ... See full document

... a nonexpansive mapping. Xu and Ori 15 introduced implicit iteration process to approximate a common fixed point of a finite family of nonexpansive mappings in a Hilbert ...an implicit ... See full document

... Some iterative algorithms for approximating fixed points of nonself nonexpansive mappings have been studied by various authors (see ...However, iterative algo- rithms for approximating fixed ... See full document

... the iterative approximation of fixed points of asymptotically nonexpansive mappings, asymptotically quasi-nonexpansive mappings, asymptoti- cally nonexpansive ... See full document

... After that, Baillon 2 proved the first nonlinear ergodic theorem: let T be a nonexpansive self-mapping defined on a nonempty bounded closed and convex set. Then for arbitrary x ∈ C, {1/n 1 n i0 T i x} converges ... See full document

... the asymptotically nonexpansive mapping, the asymptotically quasi-nonexpansive mapping, and the generalized quasi-nonexpansive mapping are all the generalized ... See full document

... Since S is nonexpansive, h ∈ R and S ◦ h ◦ T t S ◦ h for every t ≥ 0, it follows that S ◦ h ∈ R and then z ShP x ∈ K. Thus K satisfies the property ω with respect to the semigroup ϕ. Now, from Theorem 1.4, it ... See full document

... total asymptotically nonexpansive mappings as the generalization of asymptotically nonexpansive ...the nonexpansive retraction of E onto ...ically nonexpansive if there ... See full document

... Let (X, d) be a metric space. Suppose that there exists a family of metric segments such that any two points x, y in X are endpoints of a unique metric segment [x, y] ∈ ([x, y] is an isometric image of the real ... See full document

... -nonexpansive mappings to gen- eralized asymptotically quasi-φ-nonexpansive mappings and the framework of spaces is extended from a uniformly smooth and uniformly convex Banach space to ... See full document