[PDF] Top 20 New hybrid method for equilibrium problems and relatively nonexpansive mappings in Banach spaces

... real Banach space E with the dual space E ∗ . The equilibrium problem in the sense of Blum and Oettli [6] for a bifunction f : C × C → R is as follow: “ find x ∈ E such that f(x, y) ≥ 0, (y ∈ C) ... See full document

... optimization problems, but also algorithms for solving variational inequalities, for approximating equi- libria, for computing fixed points of nonlinear mappings and so on (see, ...iterative method of ... See full document

... On the other hand, motivated by Nakajo and Takahashi 14, Matsushita and Takahashi 17 reformulated the definition of the notion and obtained weak and strong convergence theorems to approximate a fixed point of a single ... See full document

... Remark . () In Theorem ., we present a strong convergence result for a system of equilibrium problems with new algorithms and new control conditions. This is comple- mentary to the main ... See full document

... a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem ...quasi-φ-asymptotically ... 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

... a new class of mappings called Bregman weak relatively nonexpansive mappings and propose new hybrid iterative algorithms for finding common fixed points of an infinite family ... See full document

... of relatively quasi-nonexpansive mappings contains the class of relatively nonexpansive ...of relatively quasi-nonexpansive mappings see, ...H, relatively ... See full document

... for all x, y, z ∈ E. Let E be a strictly convex, smooth, and reflexive Banach space, and let J be the duality mapping from E into E ∗ . Then J −1 is also single-valued, one-to-one, and surjective, and it is the ... See full document

... a new hybrid iterative scheme for finding a common element of the set of common fixed points of asymptoti- cally nonexpansive mappings and the set of solutions of an equilibrium problem ... See full document

... Huang, Strong convergence theorems for fixed point problems and generalized equilibrium problems of three relatively quasi-nonexpansive mappings in Banach spaces, J.. Zhou, Approximate p[r] ... See full document

... a new hybrid iteration method for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces, and then we discuss the ... See full document

... a new hybrid projection algorithm for finding a common element of the solutions set of a generalized mixed equilibrium problem and the fixed points set of an infinitely countable family of ... See full document

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

... strongly. T is said to satisfy condition (A) if F(T ) = ∅ and there exists a nondecreasing function f : [0, ∞ ) → [0, ∞ ) with f (0) = 0 and f (t) > 0 for all t ∈ (0, ∞ ) such that x − Tx ≥ f (d(x,F(T))) for all x ∈ ... See full document

... firmly nonexpansive-like mapping from a closed convex subset C of a smooth, strictly convex and reflexive Banach pace into itself has a fixed point if and only if C is ...an equilibrium problem and ... See full document

... From now on we denote by Ω ∗ the set of all fixed points of the mapping G. Now we prove the strong convergence theorem of algorithm 1.18 for solving problem 1.17. Theorem 3.4. Let C be a nonempty closed convex subset of ... See full document

... of nonexpansive mappings and asymptot- ically nonexpansive mappings have been studied by various authors; see, ...explicit hybrid iteration method for nonexpansive ... See full document

... Recall that the normal Mann iterative process was introduced by Mann [] in . Recently, the construction of fixed points for nonexpansive mappings via the normal Mann iterative process has been ... See full document

... an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping is studied by Takahashi and Zembayashi in 15, ...a new iterative scheme which unifies several ones ... See full document