[PDF] Top 20 Generalized viscosity approximation methods for nonexpansive mappings

... contractive mappings and apply a more gener- alized iterative method like viscosity approximation to approximate some fixed point of a nonexpansive mapping defined on a closed convex subset C of ... See full document

... using generalized viscosity approximation methods for mixed equilibrium problems and fixed point ...the generalized viscosity approximation method ...for ... See full document

... Moudafi’s viscosity approximation methods for approximating a common fixed point of a one-parameter continuous semigroup of nonexpansive mappings in CAT(0) ...of nonexpansive ... See full document

... for some t in M. The pair { f , T } is called nontrivially compatible [12] if f and T are com- patible and do have a coincidence point. The pair { f ,T } is called weakly compatible if they commute at their coincidence ... See full document

... of generalized varia- tional inequalities involving two or three three nonlinear operators has been studied by many authors; see [1-6] and the references ...The generalized variational inequali- ties are ... See full document

... relatively nonexpansive map- pings introduced in the present paper is different from the class of Bregman weak relatively nonexpansive mappings introduced in ... See full document

... Corollary 3.2. Let X be a real uniformly convex Banach space which admits a weakly sequentially continuous duality mapping J from X to X ∗ and C a nonempty closed convex subset of X. Suppose that T : C → C is a ... See full document

... The organization of this paper is as follows. In Section , we recall the notion of the metric projection, the demiclosedness principle of nonexpansive mappings and a conver- gence lemma. In Section , the ... See full document

... the viscosity approximation method to study the strong convergence problem for two one-parameter continuous semigroups of nonexpansive mappings in CAT(0) ...of nonexpansive ... See full document

... asymptotically nonexpansive map- ping, which is closely related to the theory of fixed points in Banach ...of generalized asymptotically nonexpansive ...iterative approximation problems of fixed ... See full document

... iterative methods for nonexpansive mappings have recently been applied to solve convex minimization problems; see, for example, 12–14 and the references ... See full document

... the viscosity approximation method is utilized to find a common element of the set of com- mon fixed points of a countable family of nonexpansive ... See full document

... called nonexpansive iff d(Tx, Ty) ≤ d(x, y) for all x, y ∈ ...a nonexpansive mapping T is closed and ...asymptotically nonexpansive if there exists a se- quence {k n } ⊂ [, ∞) with k n →  such that ... See full document

... Since ε is arbitrary, therefore d(p ∗ , q) = . That is, q = p ∗ ∈ F. Remark . A generalized asymptotically nonexpansive mapping is a generalized asymp- totically quasi-nonexpansive mapping. ... See full document

... resolvent-type methods cannot be extended for equilibrium ...The viscosity approximation method is one of the important methods for approximation fixed points of nonexpansive ... See full document

... called nonexpansive iff d(Tx, Ty) ≤ d(x, y) for all x, y ∈ ...a nonexpansive mapping T is closed and ...several mappings in CAT() spaces have been investigated by many authors (see also ... See full document

... on viscosity approximation method for quasi-nonexpansive mappings and split equality problems, in this paper we first intro- duce a general viscosity approximation method for ... See full document

... Theorem 3.1. Let H be a Hilbert space, C a nonempty closed convex subset of H , P the met- ric projection of H onto C, and T : C → H a nonexpansive nonself-mapping with F(T) = ∅ . Let { t n } be sequence in (0, 1) ... See full document

... We prove strong convergence of the viscosity approximation method for multivalued nonexpansive mappings in CAT(0) spaces. Our results generalize the results of Dhompongsa et al. (2012), ... See full document

... x + = λ + u + − λ + Tx n ≥ (1) Helpern [3] was the first to study the strong convergence of the iteration process (1). In 1992, Albert [4] stu- died the convergence of the Ishikawa iteration process in Banach space, ... See full document