[PDF] Top 20 Strong Convergence of Monotone Hybrid Algorithm for Hemi-Relatively Nonexpansive Mappings

... 2 Ya. I. Alber, “Metric and generalized projection operators in Banach spaces: properties and applica- tions,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, A. G. Kartsatos, ... See full document

... the strong convergence theorems for finding common fixed points of a countable family of hemi-relatively nonexpansive mappings in a uniformly convex and uniformly smooth Banach ... See full document

... Corollary 3.4. Let E be a uniformly convex and uniformly smooth real Banach space, let C be a nonempty closed convex subset of E, let f be a bifunction from C × C to R satisfying (A1)–(A4), and let T : C → C be a closed ... See full document

... obtain strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemi-relatively nonexpansive ... See full document

... “Strong convergence theorems for a generalized equilibrium problem with a relaxed monotone mapping and a countable family of nonexpansive mappings in a Hilbert space,” Fixed Point ... See full document

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

... point algorithm which was first introduced by Martinet ...weak convergence of the proximal point algorithm for maximal monotone ...point algorithm in order to obtain the strong ... See full document

... iteration algorithm for total quasi-ϕ-asymptotically nonex- pansive mapping to have the strong convergence under a limit condition in Banach ...quasi-ϕ-asymptotically nonexpansive multi-value ... See full document

... In this section, we prove strong convergence of an iterative sequence generated by the hybrid method in mathematical programming. We start with the following useful common tools. Lemma 3.1. Let C be ... See full document

... Theorem . Let C be a nonempty, closed and convex subset of a real reflexive Banach space E, f : E → R be a coercive Legendre function which is bounded, uniformly Fréchet dif- ferentiable and totally convex on a bounded ... See full document

... composite hybrid iteration process: Let H be a Hilbert space, T : H −→ H a nonexpansive mapping with F(T ) 6= /0 and f ...)−strongly monotone and k f ... See full document

... called nonexpansive if Sx − Sy ≤ x − y for all x, y ∈ ...iterative algorithm for finding a common element of the solution set of the equilibrium problem ...a relatively nonexpansive mapping S ... See full document

... 1 Y. I. Alber, “Metric and generalized projection operators in Banach spaces: properties and applications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, vol. 178 of Lecture ... 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

... GT {x, y : y ∈ Tx} is not properly contained in the graph of any other monotone operator. A method for solving the inclusion 0 ∈ Tx is the proximal point algorithm. Denote by I the identity operator on E H ... See full document

... of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of generalized ...proximal-type algorithm for ... 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 overlooked. ... See full document

... of nonexpansive mappings from C into ...a strong positive linear bounded operator with coefficient γ > 0, γ be a constant with 0 < γ < ... See full document

... Throughout this paper, we always assume that H is a real Hilbert space with the inner product ·, · and the norm · and C is a nonempty closed convex subset of H. Let S : C → C be a nonlinear mapping. In this paper, we use ... 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 spaces and ... See full document