[PDF] Top 20 Strong convergence of approximation fixed points for nonexpansive nonself mapping

... a nonexpansive mapping ...of fixed points of T; that is , Fix(T) = { x ∈ C : x = Tx } ...self- mapping f : C → C is a contraction on C if there exists a constant β ∈ (0, 1) such ... See full document

... for nonexpansive mappings in Banach spaces includ- ing Mann and Ishikawa iteration processes has been studied extensively by many au- thors to solve the nonlinear operator equations in Hilbert spaces and Banach ... See full document

... continuous mapping in Banach ...some strong convergence theorems of the proposed iteration for an asymptotically nonexpansive nonself-mapping with the condition ... See full document

... the strong convergence of the iteration process ...the convergence of the Ishikawa iteration process in Banach space, which was extended the results of Mann iteration process ... See full document

... of fixed points of nonexpansive mappings (and asymptotically nonex- pansive mappings) is an important subject in the theory of nonexpansive mappings and finds application in a number of ... See full document

... Recently, hybrid projection algorithms have been studied for the fixed point problems of nonlinear mappings by many authors; see, for example, 8–24. In 2006, Martinez-Yanes and Xu 10 proposed the following ... See full document

... stochastic approximation in the form (1.5) for finding fixed points of weakly contractive (Definition ...and nonexpansive (Definition ...square convergence and convergence almost ... See full document

... Let C be a nonempty closed convex subset of a real Hilbert space H . Let S : C ® C be an asymptotically nonexpansive map in the intermediate sense with the fixed point set F ( S ). Let A : C ® H be a ... See full document

... the strong convergence to common fixed points of two nonexpansive mappings in a Hilbert ...common fixed point of the mappings T i , i = 1, ... See full document

... common fixed points of a countable family of nonexpansive mappings is introduced and ...A strong convergence theorem of the proposed iterative scheme to a common fixed point of a ... See full document

... contractive mapping and A is a strongly positive bounded linear oper- ator on E with coefficient γ >  and  < γ < γ , for an asymptotically nonexpansive semi- group ϕ = {T (s) : s ∈ S} on compact ... See full document

... Motivated by the work of Wang [9] and earlier results of Xu and Kim [7] and Yamada [8], Miao and Li generalized (1.5) by developing the following composite hybrid iteration process: Let H be a Hilbert space, T : H −→ H a ... See full document

... problems, strong convergence (norm convergence) is often much more desirable than weak convergence, for it translates the physical- ly tangible property that the energy kx n −xk of the error ... See full document

... In this paper, motivated and inspired by the above results, we modify iteration process 1.4–1.11 by the new hybrid methods for countable families of asymptotically nonexpansive mappings and semigroups in a Hilbert ... See full document

... for all x, y ∈ C. We denote by F(T) the set of fixed points of T . We know F(T) = ∅ in the case that E is uniformly convex and C is bounded; see Browder [2], G¨ohde [9], and Kirk [13]. Common fixed ... See full document

... Theorem 1.2 (see [9, Theorem 5]). Let E be a uniformly convex Banach space whose norm is uniformly Gˆateaux differentiable and let C be a closed convex subset of E. Let S, T be nonexpansive mappings of C into ... See full document

... can also be defined as the generalization of asymptotically quasi-non-expansive mappings and nonself asymptotically nonexpansive mappings. These mappings are defined as follows. Definition 1.1. Let K be a ... See full document

... of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach ...the strong convergence of the ... See full document

... weak convergence theorems for asymptotically nonex- pansive mappings in Banach spaces without assuming any of the following conditions: i E satisfies the Opial’s condition; ii T is asymptotically regular or weakly ... See full document

... for nonself-mappings and to obtain a strong convergence theorem to a fixed point of a family of nonself nonexpansive mappings in Banach spaces more general than the spaces ... See full document