[PDF] Top 20 Strong Convergence Theorems of the CQ Method for Nonexpansive Semigroups

... and nonnegative real numbers, respectively. let C be a closed convex subset of a Hilbert space H , and Let T : C → C be a nonexpansive mapping (i.e., Tx − T y ≤ x − y for all x, y ∈ C). We use Fix(T ) to denote ... See full document

... Let E be a real Banach space. A mapping T of E into itself is said to be nonexpansive if Tx − Ty ≤ x − y for each x, y ∈ E. We denote by FixT the set of fixed points of T. A mapping f : E → E is called ... See full document

... -asymptotically nonexpansive semigroups; to modify the Halpern and Mann-type iteration algorithm [, ] for total quasi-φ-asymptotically nonexpansive semigroups; and to have the ... See full document

... totically nonexpansive semigroup on a nonempty compact convex subset C of a Banach space E into ...is nonexpansive and Fix(ϕ) = ∅ ...sunny nonexpansive retract of C and the sunny nonexpansive ... See full document

... Recently many authors want to modify the Mann iteration method (1.3) so that strong convergence is guaranteed have recently been made. Nakajo and Takahashi [8] proposed the following modification of ... See full document

... We consider the iterative scheme computing by the hybrid method some authors call the CQ- method. The following result is proved by He and Chen 3. However, the important part of the proof seems to 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

... two strong convergence theorems as regards this ...give strong convergence theorems as regards the split feasibility problem with modified CQ method, strong ... See full document

... In this paper, motivated by the iterative sequences 1.6 given by Saejung in 8 and Ishikawa 10, we introduce the modified Ishikawa iterative scheme for two nonexpansive semigroups in Hilbert spaces. Further, ... See full document

... establish strong convergence theorems for solving the fixed point problem of nonexpansive semigroups and strict pseudocontractions, and the zero-finding problem of maximal monotone ... See full document

... In a real Hilbert space, an iterative scheme is considered to obtain a common fixed point for a countable family of nonexpansive mappings. In addition, strong convergence to the common fixed point of ... See full document

... viscosity method for hierarchically approximating some common fixed point of an infinite family of nonexpansive mappings is presented; and some strong convergence theorems for solving ... See full document

... of nonexpansive mapping T in Hilbert space. The strong and weak convergence theorems to a fixed point of T are ...for strong convergence of this iteration scheme are obtained, ... See full document

... It is obvious that any b-inverse strongly monotone mapping B is 1 β -Lipschitzian. Moudafi [3] introduced the viscosity approximation method for fixed point of nonex- pansive mappings (see [4] for further ... See full document

... We note that it is the same as Mann’s iterations that have only weak convergence the- orems with implicit iteration scheme (1.3). In this paper, we introduce the following two general composite implicit iteration ... See full document

... infinitely nonexpansive self-mappings by using the hybrid method in a Hilbert space and prove that the modified Ishikawa iterative sequence converges strongly to a common fixed point of two infinitely ... See full document

... reversible semigroups of asymp- totically nonexpansive ...and convergence of fixed points for left amenable semigroups of asymptotically nonexpansive type mappings in Banach ...amenable ... See full document

... for each n ≥ 0 in a reflexive Banach space with a uniformly Gˆateaux differentiable norm such that each nonempty bounded closed and convex subset of E has the common fixed point property for nonexpansive mappings ... See full document

... iteration method is investigated for approximating fixed points of asymptotically nonexpansive ...and strong convergence theorems are established in arbitrary Ba- nach ...and ... See full document

... descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings,” in Inherently Parallel Algorithms in Feasibility and Optimization and Their ... See full document