[PDF] Top 20 Discussion on the fixed point problems with constraint inequalities

... fixed point of the mapping T is an element x ∈ Y for which Tx = x. Fixed point theory plays a crucial role in nonlinear functional analysis and many authors have studied this ...fixed point ... See full document

... converges strongly to a fixed point x ∗ of T, also the solution of a variational inequality. As a special case, this projection method solves some quadratic minimization problem. The results here improve and extend ... See full document

... In view of Corollary ., we have the following corollary on variational inequalities. Corollary . Let C be a nonempty closed convex subset of a real Hilbert space H and A : C → H be an α-inverse-strongly ... See full document

... fixed point theorems on ordered metric spaces and applied the obtained results to the study of existence and uniqueness of solutions to a class of periodic boundary value ... See full document

... variational inequalities with hierar- chical fixed point problem constraint for a countable family of nonexpansive mappings in a real Banach space, which can be viewed as an extension and improvement ... See full document

... Hence the mapping T from C × D to  C×D \{∅} satisfies all conditions in Theorem . with respect to condition A . As we apply the mapping T to the preordered set (C × D, X×Y ), which is a chain complete preordered set, ... See full document

... variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in a uniformly convex Banach space which has a uniformly Gâteaux differentiable norm, and we prove some ... 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 variational ... See full document

... where T and S are two nonexpansive mappings from a nonempty closed convex subset C of a real Hilbert space H into itself, and F(S) denotes the set of fixed points of the map- ping S. One can easily observe that VI F(S) ... See full document

... In this paper, motivated by the work of Zhou et al. [], Bnouhachem et al. [, ] and others, we give an iterative method for finding the approximate element of the common set of solutions of GMEP (.), VIP (.) and ... See full document

... all fixed points of T is denoted by F (T ), that is F(T ) = {x ∈ C | x = T ...unique fixed point in C, and for any fixed element x 0 ∈ C, Picard’s iteration x n+1 = f n (x 0 ) ... See full document

... In this paper, we propose a new iterative scheme for finding a solution of SMVIP (1.3) with the constraints of a variational inequality and a fixed point problem of a finite family of strict pseudo-contractions in ... See full document

... optimization problems, variational inequalities prob- lems, saddle point problems, the Nash equilibrium problems, fixed point problems, com- plementary problems, ... See full document

... hierarchical fixed point approach to variational inequalities,” Bulletin of the Australian Mathematical Society, ...hierarchical fixed-point problems,” Pacific Journal of Opti- ... See full document

... of fixed points of a family of finitely nonexpansive mappings, the set of solutions of mixed equilibrium problem and the set of solutions of a variational inequality problem for a β-inverse-strongly monotone ... See full document

... converges weakly to a point, which lies in VI(C, A). The literature on the VIP is quite vast and Korpelevich’s extragradient method, which is projection-based, has received great at- tention given by many ... See full document

... of fixed point sets of nonexpansive mappings,” in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications (Haifa, 2000), ... See full document

... Throughout the paper, unless otherwise specified, we assume that H is a real Hilbert space whose inner product and norm are denoted by 〈·,·〉 and || · ||, respectively, and C is a nonempty closed convex subset of H. The ... See full document

... 1. Yamada, I: The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings. In: Butnariu, D, Censor, Y, Reich, S (eds.) Inherently ... See full document

... 19. Kim, JK: Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi- φ -nonexpansive mappings. Fixed Point ... See full document