[PDF] Top 20 Fixed points, intersection theorems, variational inequalities, and equilibrium theorems

... known theorems, including Kakutani’s theorem [26] for Euclidean spaces and Himmelberg’s theorem [17] for locally convex topological vector ...these theorems were so useful in various problems in ... See full document

... The problem is to find some fixed point in C t>0 FixT t. For this, so many algorithms have been developed and under some restrictions partial answers have been obtained 6–11. Assume that F : X → X is a strongly ... See full document

... the variational inequality for an a-inverse-strongly monotone opera- tor, the set of solutions of the generalized equilibrium problems, and the set of common fixed points of an infinite family ... See full document

... for all x, y ∈ C. Evidently, the definition of the inverse strongly accretive operator is based on that of the inverse strongly monotone operator. To convey an idea of the variational inequality, let C be a closed ... See full document

... spaces, 2 ≤ p < ∞ under conditions C1, C2, and C5 or C6 as in the result of Xu and Kim. It is our purpose in this paper to modify the schemes 1.8 and 1.9 and prove strong convergence theorems for the unique ... See full document

... In this paper, we introduce a new composite viscosity iterative algorithm and prove the strong convergence of the proposed algorithm to a common fixed point of one finite family of nonexpansive mappings and another infinite ... 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

... ational inequalities, in which the ranges of the considered mappings and the underlying spaces both are preordered ...eralized equilibrium problems in preordered ... See full document

... verges weakly to p such that n→∞ lim || x n − Tx n || = 0 . The set of asymptotic fixed points of T will be denoted by F(T) . A mapping T from C into itself is said to be nonexpan- sive if ||Tx - Ty|| ≤ ||x ... See full document

... There are a substantial number of numerical methods including projection technique and its variant forms, Wiener-Hopf equations, the auxiliary principle technique, and re- solvent equations methods for solving ... See full document

... of variational inequality and the set of common fixed points of a countable family of nonexpansive mappings is introduced and ...common fixed point of a countable family of nonexpansive ... See full document

... the intersection of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of some variational inequality problems, and the set of solutions of ... See full document

... uniqueness theorems of solutions for problems ...economics equilibrium, and free boundary-valued problems, and so forth On the other hand, Bose [1], Dien [3], Ding [5], Fang et ... See full document

... of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings,” Nonlinear Analysis: Theory, Methods & Applications, ... See full document

... of variational inequalities for an inverse-strongly monotone mapping and in the set of fixed points of nonexpansive mappings or strict pseudocontractions; see [–] and the references ...of ... See full document

... Proof. By condition (1), x∈X F (x) = x∈X cl F (x). Hence in order to prove the conclusion of the theorem, it suffices to prove that x∈X clF (x) ≠ ∅ . Since L is com- pact, for the purpose, it suffices to prove that {clF (x) ... See full document

... invex equilibrium problem related to the original ...of equilibrium problems, variational-like inequalities, and variational ...invex equilibrium problems with bifunc- tion ... See full document

... several authors, see, e.g., [–] and the references therein. Very recently, Du, Karapinar and Shahzad [] established the following intersection existence theorem of coincidence points and fixed ... See full document

... fixed points is important in the study of many real world problems, including inverse problems; for instance, it is not hard to show that the split feasibility problem and the convex feasibility problem in signal ... See full document

... The variational inequality problem with respect to A and C is to find u ∈ C such that Au, v − u ≥ 0 for all v ∈ ...of variational inequality problem with respect to C and A is denoted by VI ( C, A ) ...the ... See full document