[PDF] Top 20 Strong convergence of a general algorithm for nonexpansive mappings in Banach spaces

... weakly to a unique element z of S(C, A), where S(C, A) = {u ∈ C : Au, j(v–u) ≥ , ∀v ∈ C}. The results of Yao et al. [] and Wang and Hu [] both are obtained when the underlying space is a Hilbert space. Meanwhile, ... See full document

... and strong convergence theorems for relatively nonexpansive mappings in Banach spaces which were first introduced by Butnariu et ... See full document

... real Banach space, K a nonempty closed convex subset of E, and T : K → K a ...called nonexpansive if Tx − Ty ≤ x − y for all x, y ∈ ...and strong convergence, ... See full document

... In this paper, we establish a necessary and sufficient condition for the strong convergence of nonexpansive mappings in a uniformly convex and 2-uniformly smooth Banach space. It is worth ... 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 point theorems for ... See full document

... iterative algorithm in the framework of Hilbert spaces and gave strong convergence theorem for nonexpansive ...to Banach spaces by using the generalized ...iterative ... See full document

... On the other hand, iterative approximation methods for nonexpansive mappings have recently been applied to solve convex minimization problems; see, for example, 9–11 and the references therein. Let H be a ... See full document

... finite nonexpansive mappings in Hilbert ...a Banach space. By using the Banach limit as in [19, 23], Zhou et ...the strong convergence of the iterative scheme (1.1) in certain ... See full document

... relatively nonexpansive mappings in Banach ...and strong convergence theorems to approximate a fixed point of a single relatively nonexpansive ...the strong ... 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

... in Banach spaces: properties and applications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, ...“A strong convergence theorem for relatively ... See full document

... the convergence of ...weak convergence except in a finite dimensional space. To obtain strong convergence in the setting of an infinite dimensional Hilbert or Banach spaces, ... See full document

... a strong convergence theorem with the help of our process for the class of nonexpansive mappings in general Banach spaces and apply it to get a result in uniformly convex ... See full document

... quasi-nonexpansive mappings with error members. Moreover, we will prove the strong convergence of iterative scheme to a fixed point of T (C need not to be a bounded set), requiring T to be ... See full document

... convex Banach space which admits a weakly sequentially con- tinuous duality mapping from E to E ∗ , C a nonempty closed convex subset of E which is also a sunny nonexpansive retract of E, and T : C → E a ... See full document

... Bregman nonexpansive type mappings, we refer the readers to [–, , ...Bregman nonexpansive type mappings, the assumption F(T ˆ ) = F(T) is imposed on the map T ...a Banach space ... See full document

... As we all know that if C is a nonempty closed convex subset of a Hilbert space H and P C : H → C is the metric projection of H onto C, then P C is nonexpansive. This fact actually characterizes Hilbert ... 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

... that Algorithm (1.2) only has weak convergence even for nonexpansive mappings in infinite-dimensional Hilbert spaces (see [8] for more details and the refer- ence ...dimension ... See full document

... strongly nonexpansive multi-valued mappings in reflexive Ba- nach spaces are ...conditions, strong convergence theorems for the proposed modified Halpern’s iterations are ... See full document