[PDF] Top 20 The Hybrid Extragradient Method for the Split Feasibility and Fixed Point Problems

... equilibrium problems, which arise in several branches of pure and applied sciences in a unified and general ...optimization problems, see, ...Korpelevich’s extragradient method which was ... See full document

... The iterative algorithm (.) is due to Moudafi [], by generalizing Browder’s and Halpern’s methods, who introduced viscosity approximation methods. Suzuki [] estab- lished a strong convergence theorem by using ... See full document

... If every closed convex subset of a Hilbert space is the fixed point set of its associating projection, then the split feasibility problem becomes a special case of the split common fixed p[r] ... See full document

... new 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 strict ... See full document

... the split feasibility problem (SFP) in finite- dimensional Hilbert spaces for modeling inverse problems which arise from phase re- trievals and in medical image reconstruction ...a point x ∗ ... See full document

... type extragradient method for finding a common element of the solution set of the SFP and the set Fix(T) of asymptot- ically quasi-nonexpansive mappings and Lipshitz continuous mappings in a real Hilbert ... See full document

... solving split feasibility and fixed point problems involved in pseudo-contractive mappings in real Hilbert ...the split feasibility and fixed point problems involved ... See full document

... The SCFP is a natural extension of the SFP and of the convex feasibility problem. The SCFP was firstly considered by Censor and Segal in [] where S and T are directed op- erators which include the orthogonal ... See full document

... the extragradient method for finding a common element of the set of solutions of a generalized mixed equilibrium prob- lem, the set of fixed points of nonexpansive mappings and the set of solutions of an ... See full document

... the split common fixed-point problem (SCFP) introduced by Censor and ...projection method, we propose a cyclic iterative scheme and prove its strong convergence to a solution of SCFP under some mild ... See full document

... the split feasibility problem, which is to find an element of a closed convex subset of the Euclidean space whose image un- der a linear operator is an element of another closed convex subset of a Euclidean ... See full document

... The split common fixed point problem for directed ...The split common fixed-point problem for demi-contractive ...for split feasibility problems in Hilbert ...the ... See full document

... a point, which lies in VI(C, ...Korpelevich’s extragradient method, which is projection-based, has received great at- tention given by many researchers working on nonlinear programming, who improved ... See full document

... a hybrid viscosity iterative method to ap- proximate a common solution of a split equilibrium problem and a fixed point problem of a finite collection of nonexpansive mappings; Onjai-uea and ... See full document

... a modified forward–backward splitting method, we propose a viscosity iterative algorithm (see (3.4) below). Under suitable conditions, some strong convergence theorems of the sequence generated by the algorithm to ... See full document

... The solution set of the variational inequality 1.1 is denoted by VIA, C. Variational inequality theory has been studied quite extensively and has emerged as an important tool in the study of a wide class of obstacle, ... See full document

... the split feasibility problem and split common null point problem in the setting of a Banach ...using hybrid methods and Halpern-type methods and under suitable conditions, some strong ... See full document

... minimization problems; see, for example, 21–24 and the references ...minimization problems have a great impact and influence in the development of almost all branches of pure and applied ...the fixed ... 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

... of fixed points of nonexpansive mappings (asympto- tically nonexpansive mappings), and of common fixed points of nonexpansive semi- groups (asymptotically nonexpansive semi-groups) is an important problem ... See full document