[PDF] Top 20 On the hierarchical variational inclusion problems in Hilbert spaces

... To overcome this drawback, inspired by the method studied by Yamada et al. [, ], Maingé [] and Kraikaew et al. [], we investigate a more general variant of the scheme proposed by Maingé [], Kraikaew et al. [] ... See full document

... Lemma 2.7 Let F be a L-Lipschitzian and h-strongly monotone operator on a none- mpty closed convex subset C of a real Hilbert space H with 0 <h ≤ L and 0 <t < 2h/ L 2 . Then S = (I - tF): C ® C is a ... See full document

... equality variational inclusion problem and the common fixed point set of a family of nonexpansive mappings, which is also an unique solution of a variational inequality as an optimality condition for ... See full document

... 33. Kim, JK: Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi- φ -nonexpansive mappings. Fixed Point Theory Appl. 2011, ... See full document

... In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple–sets split variational inequality problems. The sequence of the proposed iterative ... See full document

... Inspired and motivated by the recent research going on in this area, in this paper, we consider the existence theorem and a method for finding solutions for the systems of nonlinear general set-valued mixed ... See full document

... the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings,” in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, ... See full document

... to variational inclusion, equilibrium and fixed point problems have been recently extensively investigated based on iterative methods; see [–] and the ref- erences ...complex problems, which ... See full document

... split variational inclusion and nonexpansive semigroups in Hilbert ...split variational inclusion and the set of common fixed points of one-parameter nonexpansive semigroups, which also ... See full document

... In 1997, Combettes and Hirstoaga 14 introduced an iterative method of finding the best approximation to the initial data when EPΘ is nonempty and proved a strong convergence theorem. Subsequently, S. Takahashi and W. ... See full document

... Variational inequalities were initially investigated by Kinderlehrer and Stampacchia in [], and have been widely studied by many authors ever since, due to the fact that they cover as diverse disciplines as ... See full document

... mathematical problems and have wide applications in the fields of optimization and con- trol, economics, transportation equilibrium and engineering ...ear variational inequalities as well as operator ... See full document

... We denote the set of solutions of GMEP (.) by GMEP(Θ, ϕ, A). The GMEP (.) is very general in the sense that it includes, as special cases, optimization problems, variational in- equalities, minimax ... See full document

... Corollary 3.4 see Peng et al. 9. Let H be a real Hilbert space, let F be a bifunction from C×C → R satisfying (A1)–(A4) and let S be a nonexpansive mapping on H. Let A : H → H be an α- inverse-strongly monotone ... See full document

... ordered variational inclusion problems (inequalities, systems, and equations) in ordered Banach spaces; for example, in , Li has introduced and studied the approximation algorithm and the ... See full document

... Remark . The strong nonexpansiveness of operators T and S in Theorem . can be applied to the cases when the operators T and S are not only firmly nonexpansive, but with relaxation of being firmly nonexpansive and ... See full document

... We design synchronal algorithm and cyclic algorithm based on the general iterative algorithm proposed by Tian in 2010 for finding the common fixed point x * of finite family of strict pseudo-contractive mappings which is ... See full document

... In [22], Kazmi and Rizvi proposed iterative scheme and proved that such sequences converges strongly to a common solution of split variational inclusion problem and fixed point problem. Note that, in fact, ... See full document

... Tx − Ty ≤ x − y for all x, y ∈ C. The set of fixed-points of T is denoted by the set FixT : {x ∈ C : Tx x}. It is well known that if FixT / ∅, then FixT is closed and convex. Given nonexpansive mapping V : C → C, ... See full document

... Remark 2.21. For appropriate and suitable choices of f , T , M, g, and X, it is easy to see that the problem (2.25) includes a number of quasi-variational inclusions, general- ized quasi-variational ... See full document