[PDF] Top 20 The convergence analysis of the projection methods for a system of generalized relaxed cocoercive variational inequalities in Hilbert spaces

... Variational inequalities are one of the most interesting and intensively studied classes of mathematical problems and there exists a considerable amount of literature [–] on the approximate solvability ... See full document

... jection methods, and its special form can be applied to the convergence analysis for the projection methods in the context of the approximation solvability of the SNVID prob- lems ... See full document

... nonlinear variational inequalities as well as of nonlinear equations, in several fields such as applied mathematics, mathematical programming, mathematical finance, control theory and optimization, ... See full document

... the generalized f-projection operator and proposed iterative method of approximating solutions for a class of generalized variational inequalities in Banach ...the generalized ... See full document

... tors, generalized m-accretive mappings, H-accretive operators, (H, h)-monotone operators, and A-monotone ...nonlinear variational inclusion systems with (A, h)-accretive mappings in q-uniformly smooth ... See full document

... of generalized variational inequalities involving multivalued relaxed monotone operators and single-valued nonexpansive mappings in the framework of Hilbert ...the convergence ... See full document

... nonconvex variational inequalities based on the uni- formly prox-regular ...nonconvex variational inequalities, which shows projection technique can be extended to nonconvex ... See full document

... This alternative formula enables us to suggest and analyze a two-step explicit projection method for solving system (.), and this is the main motivation of our next result. Theorem . Let C be a nonempty ... See full document

... of variational inequalities which were difference from the sense of Pang [18] and developed some iterative algorithms for approximating the solutions of these systems in Hilbert spaces base on ... See full document

... for variational inclusion (operator equation) problems involving strongly monotone and relaxed cocoercive map- pings under suitable second order and regularity assumptions is an increasing interest, ... See full document

... new system of generalized nonlinear relaxed cocoercive in- equality problems and construct an iterative algorithm for approximating the solutions of the system of generalized ... See full document

... Variational inequalities introduced by Stampacchia 1 in the early sixties have had a great impact and influence in the development of almost all branches of pure and applied ...the variational ... See full document

... intersection of two halfspaces is easily computable. In addition, we propose a modified version of our algorithm that is to find a solution of VI which is also a fixed point of a given nonexpansive mapping. We establish ... See full document

... Recently, variational inequalities, fixed point problems, and zero point problems have been investigated by many authors based on iterative methods; see, for example, [–] and the references ... See full document

... new system of nonlinear variational inclusions in Hilbert ...a Hilbert space with norm denoted by · i , A i : H i → H i , F i : p j1 H j → H i are single-valued mappings, and M i : H i → 2 H i ... See full document

... their convergence properties and obtaining useful stopping rules for iterative ...a generalized MVI (which was defined on the whole space) and used those functions to obtain error bounds for ...the ... See full document

... new system of general variational inequalities in Banach ...this system of variational inequalities and fixed point problems concerning the nonexpansive mapping is ...the ... See full document

... For this purpose, in this paper, we first suggest and analyze an implicit extragradient method. It is shown that the net defined by this implicit extragradient method converges strongly to the unique solution of HVIC, A, ... See full document

... N(w, y), g (v) − g(u) ≥ 0, ∀ v ∈ K (u). (2.13) This problem is called the multivalued quasi-variational inequality for fuzzy mappings. In the case of classical multivalued mappings this problem has been considered ... See full document

... 2. Stampacchia, G: Formes bilinéaires coercitives sur les ensembles convexes. C. R. Acad. Sci. Paris 258, 4413-4416 (1964) 3. Shi, P: Equivalence of variational inequalities with Wiener-Hopf equations. ... See full document