[PDF] Top 20 Strong convergence theorems for common solutions of variational inequality and fixed point problems

... 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 over ... See full document

... weak convergence, in general, even for nonexpansive map- ...obtain strong convergence, some modifications of the normal Mann ’ s iteration algorithm has been ... See full document

... weak convergence. In order to obtain strong convergence theorem, very recently, Zeng and Yao [] further introduced a new extragradient method for finding a common element of the set of fixed ... See full document

... a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping ... See full document

... the problems of finding a common element in the set of solution of variational inequalities for an inverse-strongly monotone mapping and in the set of fixed points of nonexpansive mappings or strict ... See full document

... equilibrium problems is an important branch of optimization theory and nonlinear functional ...Numerous problems in physics, optimization, transporta- tion, signal processing, and economics are reduced to ... See full document

... tion, and economics reduce to finding a solution of (.); see [–]. In , Combettes and Hirstoaga [] introduced an iterative scheme of finding the best approximation to the initial data when EP(F) is nonempty. ... See full document

... a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of variational inequalities for a strongly positive linear bounded operator ... See full document

... Many problems in mathematics, in physical sciences and in real-world applications of various technological innovations can be modeled as a convex feasibility problem ...a point in the intersection of ... See full document

... a fixed point of T, FT : {x ∈ DT : Tx x} is a zero of A, NA : {x ∈ DA : Ax ...the solutions of the equation Ax 0 correspond to the equilibrium points of some evolution ...approximating fixed ... See full document

... a common solution of (P1) and (P2) (i.e., some point belong- ing to F ∩ G ), and show a strong convergence theorem in a uniformly smooth and strictly convex Banach space with the Kadec-Klee ... See full document

... a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert ...some strong convergence theorems which ... See full document

... a strong convergence result for finding common element of the set of fixed points of strictly pseudocontractive mappings and the set of solutions of variational inequality ... See full document

... Korpelevich’s extragradient method has extensively been studied in the literature for solving a more general problem that consists of finding a common point that lies in the solution set of a ... See full document

... classical variational inequality (1.2) and fixed point problem of nonexpansive mappings have received rapid development, see, for example, [1-17] and the references ...for variational ... See full document

... above convergence theorems are ...a common solution to the zero point problems and fixed point problems based on hybrid iterative methods with ...errors. Strong ... See full document

... optimization problems, economics and transportation. The theory of variational inequalities has emerged as a rapidly growing area of research because of its applications; see [–] fore more details and ... See full document

... a common element of the solution set of a variational inequality problem, the solution set of a general system of variational inequalities, and the fixed-point set of a strictly ... See full document

... of variational inequality and the set of common fixed points of a countable family of nonexpansive mappings is introduced and ...A strong convergence theorem of the proposed ... See full document

... whose solutions correspond to the equilibrium points of (.). An early fundamental result in the theory of accretive operators, due to Browder [], states that the initial value prob- lem (.) is solvable if A ... See full document