[PDF] Top 20 An Iterative Method for Generalized Equilibrium Problems, Fixed Point Problems and Variational Inequality Problems

... Let C be a nonempty closed convex subset of a real Hilbert space H and let Φ : C × C → R be a bifunction, where R is the set of real numbers. Let Ψ : C → H be a nonlinear mapping. The generalized ... See full document

... viscosity iterative method for finding a common element of three solution sets: (i) finite split generalized equilibrium problems; (ii) finite variational inequality ... See full document

... new method for a system of generalized equilibrium problems, system of variational inequality problems, and fixed point problems by using S-mapping ... See full document

... an iterative scheme for finding a common element of the set of fixed points of a k- strictly pseudocontractive mapping, the set of solutions of the variational inequality for an inverse- ... See full document

... a generalized equilibrium prob- lem and the set of common fixed points of a finite family of asymptotically κ-strict pseu- docontractive mappings in the intermediate sense, utilizing the method in ... See full document

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

... optimization problems, variational inequalities, minimax problems, and Nash equilibrium problems; see, for example, ...system generalized equilibrium ... See full document

... hybrid method we prove a strong convergence theorem for finding a common element of the set of fixed point problems of a finite family of i -strictly pseudocontractive mappings and the set of ... See full document

... fixed point problem of finitely many nonexpansive ...extragradient method [], the hybrid steepest-descent method in [], the viscosity approximation method, and the averaged mapping approach to ... See full document

... inclusion problems, saddle point problems, variational inequality problems, minimization problems, the Nash equilibria in noncooperative games, vector equilibrium ... See full document

... hierarchical fixed point approach to variational inequalities,” Bulletin of the Australian Mathematical Society, ...an iterative method for hierarchical fixed-point ... 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 ... See full document

... of variational inequalities (2.1), (2.2), and in the fixed point set of nonex- pansive ...direction, fixed point problems of nonexpansive mappings and solution problems of ... See full document

... is called the resolvent operator associated with M, where λ is any positive number and I is the identity mapping. In the worth mentioning that the resolvent operator is nonexpan- sive, -inverse-strongly monotone and ... See full document

... hybrid iterative scheme ...for generalized mixed equi- librium problems and the set of common fixed points of a sequence of nonexpansive ...of variational inequalities under some mild ... See full document

... extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality ... See full document

... Recently, Plubtieng and Punpaeng [] and Ceng et al. [, ] considered some iterative methods for VIP (.) and its extended versions and got some strong convergence theo- rems. As a generalization of VIP ... See full document

... Theorem 3.2. Let C be a nonempty closed convex subset of H. Let F be a bifunction from C × C to R satisfying (A1)–(A4) and let S be a nonexpansive mapping of C into H. Let A : C → H be an α- inverse strongly monotone ... 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

... 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