[PDF] Top 20 A Hybrid Extragradient Method for Solving Ky Fan Inequalities, Variational Inequalities and Fixed Point Problems

... is a real sequence in [0, 1]. The Mann iteration has been extensively investigated for nonexpansive mappings. One of the fundamental convergence results is proved by Reich [11]. In an infinite-dimensional Hilbert space, ... See full document

... (4) Variational inequality theory has emerged as an important tool in studying a wide class of obstacle, unilateral and equilibrium problems, which arise in several branches of pure and applied sciences in ... See full document

... “An extragradient method for fixed point problems and variational inequality problems,” Journal of Inequalities and Applications, ...space,” Fixed ... See full document

... a hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family ... See full document

... a hybrid extragradient method for finding a common element of the solution set of a variational inequality problem, the solution set of a general system of variational ... See full document

... In this paper, motivated by the above facts, we introduce and study two implicit iter- ative algorithms and two explicit iterative algorithms by hybrid viscosity approximation methods for finding a common element ... See full document

... steepest-descent method for solving the VI(F, C). Assume that F is an η-strongly mono- tone and κ-Lipschitzian mapping with κ > , η >  on C. An equally important problem is how to find an approximate ... See full document

... extragradient method for solving the VIP in [23] is extended to develop our composite inertial subgradient–extragradient method with line-search process for solving the VIP and ... See full document

... the variational inequalities are equivalent to the fixed-point problems, the origin of which can be traced back to Lions and Stampacchia ...iterative method for solving ... See full document

... of solving a system of variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in Banach spaces, we propose a two-step relaxed ... See full document

... for solving variational inequalities and related optimization problems; see ...fixed point theory has played an important role in the development of various algorithms for solving ... See full document

... The variational inequality problem is a fundamental problem in variational analysis and, in particular, in optimization ...gradient method for constrained optimization, ... See full document

... “The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings,” in Inherently Parallel Algorithms in ... See full document

... of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous ...an ... See full document

... that variational inequality ...fixed point problem. The element x ∈ C is a solution of variational inequality ...fixed point equation x = Proj C (x – λAx), where λ >  is a ...of ... 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 ... See full document

... Now, it is natural to be motivated by the result of Wang and Chen, in view of the discussions above, to ask whether one can determine all the pairs r, s with r > s such that either one of the inequalities ... See full document

... Similar problems have been studied extensively ...optimization problems, variational inequalities, minimax problems, the Nash equilibrium problem in noncooperative games and others; ... See full document

... Cartwright and Field [9] first proved the validity of (1.2) for r = 1, s = 0. For other extensions and refinements of (1.2), see [3, 13, 18, 19]. Inequality (1.3) is commonly referred to as the additive Ky Fan’s ... See full document

... D.Cartwright and M.Field[6] first proved the validity of (1.2) for r = 1, s = 0. For other extensions and refinements of (1.2), see [3], [7],[11] and [12]. (1.3) is commonly referred as the additive Ky Fan’s ... See full document