[PDF] Top 20 The methods for variational inequality problems and fixed point of κ-strictly pseudononspreading mapping

... Let C be a nonempty closed convex subset of a real Hilbert space H. Recall that the map- ping T : C → C is said to be nonexpansive if Tx – Ty ≤ x – y for all x, y ∈ C. In , Kohsaka and Takahashi [] introduced the ... See full document

... Variational inequality problems have emerged as an effective and powerful tool for studying a wide class of problems which arise in economics, finance, image reconstruc- tion, ecology, ... See full document

... Iterative methods for nonexpansive mappings have recently been applied to solve convex minimization problems; see, for example, 21–24 and the references ...minimization problems have a great impact ... See full document

... for variational inequality problems over the intersection of the fixed point sets of nonexpansive ...Iterative methods for finding minimum-norm fixed points of nonexpansive mappings ... See full document

... numerical methods including projection technique and its variant forms, Wiener-Hopf equations, the auxiliary principle technique, and re- solvent equations methods for solving variational ... See full document

... However, algorithm (1.2) cannot be used to solve VIP when f is monotone and k-Lipschitz continuous, which can be seen from the counterexample in [43]. During the last decade, many authors devoted their attention to ... See full document

... The variational inequality problem was initially introduced and studied by Stampacchia [] in ...years, variational inequality problems have been extended to study a large variety of ... See full document

... for variational inequality problems, mixed equilibrium problems, and fixed point problems of strictly pseudocontractive mappings in Hilbert spaces,” Fixed ... See full document

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

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

... Note that the class of -strict pseudo-contractions strictly includes the class of nonex- pansive mappings, that is T is nonexpansive if and only if T is 0-strict pseudo-contractive. If = 1, T is said to be ... See full document

... equilibrium problems, a variational inequality problem for an inverse strongly monotone mapping and common fixed points of a finite family of strictly pseudo contractive ... See full document

... of κ-strictly pseudocontractive includes the class of nonexpansive mappings as a special ...of κ-strictly pseudocontractive mappings was intro- duced by Browder and Petryshyn []; for ... See full document

... fixed point theory involving the modified variational inclusion and introduce iterative scheme for finding a common element of the set of fixed points of a κ-strictly pseudononspreading ... See full document

... has received much attention due to its applications in signal processing and image recon- struction with particular progress in intensity modulated radiation therapy [–]. Note that the involved operator g is a bounded ... See full document

... monotone mapping T : H → 2 H is said to be maximal if the graph of G(T ) of T is not properly contained in the graph of any other monotone ...set-valued mapping T : H → 2 H is said to be monotone if, for ... See full document

... common point of a solution of two variational inequality problems for continuous monotone map- pings in a uniformly smooth and strictly convex real Banach space E which also enjoys the ... See full document

... of variational inequality problems for an inverse-strongly monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings in a real Hilbert ... See full document

... Theorem 3.6. Let C be a nonempty closed convex subset of a uniformly smooth and uniformly convex Banach space E. Let T : E → 2 E ∗ be a maximal monotone operator with domain DT C, S : C → C be a relatively nonexpansive ... See full document

... We introduce an iterative scheme by the viscosity iterative method for finding a common element of the solution set of an equilibrium problem, the solution set of the variational inequality, and the ... See full document