[PDF] Top 20 An Extragradient Method for Fixed Point Problems and Variational Inequality Problems

... new extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality ... See full document

... of fixed points of an infinite family of nonexpansive mappings, the set of solutions of the variational inequality of a monotone mapping, and the set of solutions of a mixed equilibrium ...solves ... See full document

... In this paper, we establish a new iterative algorithm by combining Nadezhkina and Takahashi’s modified extragradient method and Xu’s algorithm. The mentioned iterative algorithm presents the common solution ... See full document

... self-adaptive method for solving monotone variational inequality problems and quasi-nonexpansive fixed point problems in a Hilbert ...subgradient extragradient ... See full document

... of fixed points of a demicontractive mapping and the set of solutions of a mixed equilibrium ...an extragradient method for solving the mixed equilibrium problems and the fixed ... See full document

... hybrid extragradient iterative method for finding a common element of the set of points satisfying the Ky Fan inequalities, variational inequality and the set of fixed points of a ... See full document

... new extragradient method for finding a common element of the set of fixed points of a nonex- pansive mapping and the set of solutions of a variational inequality ... See full document

... fixed point problem (SCFPP) which is to find a common element of a family of operators in one space such that its image under a linear transfor- mation is a common fixed point of another family of operators in ... See full document

... known variational in- equality problem (VIP), which find lots of applications in sparse reconstruction, image reconstruction, traffic and transportation systems, is to get x ∗ ∈ C with Ax ∗ , x – x ∗ ≥ 0 ∀ x ∈ ...the ... 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 ... 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

... the variational inequalities for monotone mappings in the framework of Hilbert spaces and Banach spaces has been intensively studied by many authors; see, for instance, 2–4 and the references cited ... See full document

... viscosity method for finding a common element of the set of solutions of a finite family of split generalized equilibrium problems, variational inequality problems and the set of common ... See full document

... librium problems in finite-dimensional ...approximate method for solving the equilibrium problem and proved the strong convergence theorem for approximating the solutions of the equilibrium ... See full document

... new extragradient method ...common fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem, and the solution set of the classical variational inequality ... See full document

... hierarchical fixed point approach to variational inequalities,” Bulletin of the Australian Mathematical Society, ...iterative method for hierarchical fixed-point ... See full document

... s extragradient method [6], Nadezh- kina and Takahashi [7] introduced an iterative scheme, called extragradient method, for finding an element of F(S) ∩ Ω and established the weak convergence ... See full document

... certain conditions, which is the key to the convergence of the algorithm. There are several studies on the descent direction. To our knowledge, just five descent directions are found so far (see [, –]). In this ... See full document

... 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 inequalities, and ... See full document

... Evidently, the class of multi-valued demicontractive mappings properly includes the class of multi-valued quasi-nonexpansive mappings. The class of demicontractive mappings is impor- tant because several common types of ... See full document