[PDF] Top 20 Strong Convergence of an Iterative Method for Equilibrium Problems and Variational Inequality Problems

... Numerous problems in physics, optimization, and economics reduce to find a solution of equilibrium ...the equilibrium problems in Hilbert space, see, for instance, Blum and Oettli 1, Combettes ... See full document

... hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of ... See full document

... Throughout this paper, we assume that H is a real Hilbert space with zero vector θ, whose inner product and norm are denoted by 〈·, ·〉 and || · ||, respectively. The sym- bols N and ℝ are used to denote the sets of ... See full document

... (1) Theorem 3.1, Corollary 3.2, Corollary 3.3, and Corollary 3.4 improve and develop the corresponding results, which were obtained recently by many authors in various references, for example, see [2,3,7-9,11-18,24,30]. ... See full document

... new iterative scheme for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings, the set of common solutions to a system of generalized mixed equilibrium ... See full document

... an iterative process for finding a common element of the set of common fixed points of infinitely many nonexpansive mappings, the set of solutions of ...the variational inequality problem for an ... See full document

... We next show the uniqueness of a solution of the variational inequality (2.1). Sup- pose both x ˜ ∈ F(S) and ˆ x ∈ F(S) are solutions to (2.1). Not lost generality, we may assume there is a positive number ... See full document

... new iterative algorithms with variable coefficients for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of the variational inequality ... See full document

... There are a substantial number of numerical methods including projection technique and its variant forms, Wiener-Hopf equations, the auxiliary principle technique, and re- solvent equations methods for solving ... See full document

... mixed equilibrium problems include fixed- point problems, optimization problems, variational inequality problems, Nash equilibrium problems, and the ... See full document

... Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory ...Zegeye, Strong ... See full document

... the variational inequality (3). It is well known that the variational inequality theory has emerged as an important tool in studying a wide class of obstacle, unilateral, and ... See full document

... the equilibrium problem and the set of the variational inequality for an inverse-strongly monotone operator and the set of fixed points of relatively quasi- nonexpansive mappings in a Banach ...a ... See full document

... Variational inequality problems have emerged as an effective and powerful tool for studying a wide class of problems which arise in economics, finance, image reconstruc- tion, ecology, ... See full document

... Let H be a real Hilbert space with the inner product and the norm being denoted by ·, · and · , respectively. Let C be a nonempty, closed, and convex subset of H and let F be a bifunction of C × C into R, where R denotes ... See full document

... the strong convergence theorem by the hybrid method for finding a common element of the set of fixed points of a finite family of nonspreading mappings and the set of solutions of a finite family of ... See full document

... Iterative methods for nonexpansive mappings have recently been applied to solve convex minimization problems; see [10-15] and the references therein. A typical problem is to mini- mize a quadratic function ... See full document

... 36. Wittmann, R: Approximation of fixed points of non-expansive mappings. Arch. Math. 58, 486-491 (1992) 37. Moudafi, A: Viscosity approximation methods for fixed-points problems. J. Math. Anal. Appl. 241, 46-55 ... See full document

... composite iterative method for finding a fixed point of a strictly pseudocontractive mapping in Hilbert ...the strong convergence of the sequence generated by the proposed iterative ... See full document

... to variational inclusion, equilibrium and fixed point problems have been recently extensively investigated based on iterative methods; see [–] and the ref- erences ...complex ... See full document