[PDF] Top 20 Convergence theorems for finding zero points of maximal monotone operators and equilibrium problems in Banach spaces

... generalized equilibrium problems include fixed point problems, optimization prob- lem, monotone inclusion problems, saddle point problems, variational inequality prob- lems, ... See full document

... of finding a common element in the fixed point set of a strict pseudocontraction and in the zero set of a nonlinear mapping which is the sum of a maximal monotone operator and a inverse ... See full document

... optimization problems, variational inequalities, minimax problems, Nash equilibrium problem in noncooperative games, and others; See, for example, 1, 2, 4, 6–9, 14–17 which are references ... See full document

... strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a hemirelatively nonexpansive mapping and for ... See full document

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

... of finding zero points for maximal monotone operators plays an impor- tant role in ...such problems in several settings, (see ... See full document

... 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 hemirelatively nonexpansive mapping in ... 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

... article, zero points of the sum of a maximal monotone operator and an inverse-strongly monotone mapping, solutions of a monotone variational inequality, and fixed points ... See full document

... strong convergence theorem for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of ... See full document

... of zero points of A + B and F, respectively. A strong convergence theorem is established under appropriate conditions imposed on the ...mixed equilibrium problems and the set of fixed ... See full document

... the equilibrium problem in a Hilbert space or in a Banach space, for instance, ...mixed equilibrium problem and the set of fixed points for a closed φ -nonexpansive mapping by using the sunny ... See full document

... A Banach space E is uniformly convex if and only if δ(ε) >0 for all ε Î (0, ...A Banach space E is said to be p-uniformly convex if there exists a constant c >0 such that δ(ε) ≥ cε p for all ε Î [0, ... See full document

... for finding a common element in the fixed point set of strict pseudocontractions and in the zero point set of the operator which is the sum of inverse strongly- monotone operators and ... See full document

... strong convergence theorem for fixed points of sequence for multivalued nonexpansive mappings and a zero of maximal monotone operator in Banach ... See full document

... Corollary 2.3. Let C be a nonempty closed convex subset of a real Hilbert space H. Let F be a bifunction from C × C to R which satisfies (A1)–(A4). Let A : C → H be an α-inverse-strongly monotone mapping and S : C ... 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 a nonempty ... See full document

... sunny iff for each x ∈ C and t ∈ (, ), we have Q(tx + ( – t)Qx) = Qx; sunny nonexpansive retraction iff Q sunny, nonexpansive and contraction. K is said to be a nonexpansive re- tract of C if there exists a nonexpansive ... See full document

... convex Banach spaces, they proved that if C is nonempty bounded closed and convex, then every asymptotically nonexpansive self-mapping T on C has a fixed ...strong convergence of iterative algorithms ... See full document

... projection operators in Banach spaces: properties and applications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, ...strong convergence ... See full document