[PDF] Top 20 On solutions of a system of variational inequalities and fixed point problems in Banach spaces

... of variational inequalities has been used as a tool to study the Nash equilibrium problem for a finite or infinite number of players; see, for ex- ample, [–] and the references ...using variational ... See full document

... of solutions of GSVI ...convex Banach space which has a uniformly Gâteaux differentiable ...smooth Banach space X in [, Theorem ...convex Banach space X having a uniformly Gâteaux ... See full document

... It is clear that V( , x) is continuous and the map x ↦ V( , x) and ↦ V( , x) are convex and (∥∥ - ∥x∥) 2 ≤ V(, x) ≤ (∥∥ + ∥x∥) 2 . We remark that the main Lyapunov functional V was first introduced by Alber [35] and its ... See full document

... finding solutions of GSVI ...smooth Banach space, and then another composite Mann iterative algorithm in a uniformly convex Banach space having a uniformly Gâteaux differentiable ... See full document

... general system of variational inequalities, where A, B : C → H are two nonlinear mappings, λ >  and μ >  are two ...of solutions of variational inequality problem ... See full document

... variational inequalities. This problem contains many important problems as special cases, for instance, optimization, Nash equilibrium, complementarity, and fixed-point problems ... See full document

... the variational inequalities, we have the problem of find- ing the fixed points of nonexpansive mappings, which is the subject of current interest in functional ...of solutions of variational ... See full document

... of solutions of modification of a system of variational inequalities problems in a uniformly convex and 2-uniformly smooth Banach ...of solutions of variational ... See full document

... convex Banach space with a uniformly Gâteaux differentiable norm, Chen and Song [] studied the strong conver- gence of the implicit and explicit viscosity iteration processes for a nonexpansive semi- group S = ... See full document

... smooth Banach space and T : C → C a nonexpansive mapping with a fixed ...each fixed u ∈ C and every t ∈ 0, 1, the unique fixed point x t ∈ C of the contraction C x → tu 1 − tTx ... See full document

... a Banach space E with the dual E ∗ , let T : C → E ∗ be a continuous mapping, and let S : C → C be a relatively nonexpansive ...the variational inequality for short, VIT − f, C: find x ∈ C such that y − x, ... See full document

... 28 Ya. I. Alber, “Metric and generalized projection operators in Banach spaces: properties and applications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, A. G. ... See full document

... common fixed points of a finite family of quasi-φ-nonexpansive mappings, the set of common solutions of a finite family of equilibrium problems, and the set of common solutions of a finite ... See full document

... of problems arising in pure and applied sciences including elas- ticity, optimization, economics, transportation, and structural analysis, see, for exam- ple, [1–8, 10–37] and the references ...classical ... See full document

... More recently, Kumam and Katchang 6, W. Kumam and P. Kumam 7, Li and Su 8 and many others see, e.g. 9–12 and the references contained in them studied the problem of fixed point approximations and ... See full document

... concrete problems in machine learning, linear inverse and many nonlinear problems such as convex programming, split feasibility problem, see [3, 4, 15, ...of solutions of (1) is supposed to be ... See full document

... In this paper, we introduce an general iterative algorithm for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and of the set of solutions to the ... See full document

... study variational-like inclusions involving infinite family of set-valued mappings and their equivalence with resolvent ...that variational-like inclusions in real Banach spaces are equivalent ... See full document

... of variational inequalities (2.1), (2.2), and in the fixed point set of nonex- pansive ...direction, fixed point problems of nonexpansive mappings and solution ... See full document

... known variational inequality problems and variational-like inequality problems in [1, 2, 3, 4, 7, 11, 12, 13] as special cases of the generalized nonlinear variational-like inequality ... See full document