[PDF] Top 20 Convergence of iterative algorithms for a generalized variational inequality and a nonexpansive mapping

... of variational inequalities ...of nonexpansive mappings and solution problems of generalized variational in- equalities are investigated based on a composite approximate iterative ... See full document

... It is well known that if C is nonempty bounded closed and convex subset of H, then the fixed point set of the nonexpansive mapping S is nonempty, see [6] more details. Recently, fixed point problems of ... See full document

... a variational inequality problem which is defined over the set of intersections of the set of fixed points of a ζ -strictly pseudocontractive mapping, the set of fixed points of a nonexpansive ... See full document

... Recently, Iemoto and Takahashi considered a weak convergence iterative scheme for a nonspreading mapping and a nonexpansive mapping in Hilbert spaces.. In this paper, we suggest two hybr[r] ... See full document

... two generalized variational inequalities ...some iterative schemes for solving the variational inequality ...several iterative schemes for solving the variational ... See full document

... new iterative scheme by hybrid method for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings, the set of common solutions to a system of ... See full document

... the generalized split feasibility problems (GSFP): finding an element that solves a variational inequality problem such that its image under a given bounded linear operator is in a fixed point set of a ... See full document

... the variational inequality problem is denoted by VI(C, ...extragradient iterative process was first introduced by Korpelevich in ...asymptotically nonexpansive mapping in the ... See full document

... where θ is a zero vector in H. The set of solutions to variational inclusion (1.1) is denoted by I(A, M). When A = 0, then (1.1) becomes the inclusion problem introduced by Rockafellar [1]. Let ϕ : C → H be a ... See full document

... Theorem . [, Theorem .] Let C be a nonempty closed convex subset of a real Hilbert space H, and let N ≥  be an integer. Let φ be a bifunction from C × C to R satisfying (A)-(A), and let A be an ... See full document

... classical variational inequality ...of nonexpansive mappings have received rapid development, see, for example, [1-17] and the references ...for variational inequality problems and ... See full document

... of variational inequality and the set of common fixed points of a countable family of nonexpansive mappings is introduced and ...strong convergence theorem of the proposed iterative ... See full document

... 4 J.-C. Yao and O. Chadli, “Pseudomonotone complementarity problems and variational inequalities,” in Handbook of Generalized Convexity and Generalized Monotonicity, vol. 76 of Nonconvex Optimization ... See full document

... descent algorithms for solving variational inequality VIC, F of finding a point x ∗ ∈ C such that Fx ∗ , x − x ∗ ≥ 0, for all x ∈ C, where C is the set of fixed points of a strict pseudocontraction, ... See full document

... It is well known that any complete, simply connected Riemannian manifold having non- positive sectional curvature is a CAT() space. Other examples include Pre-Hilbert spaces, R-trees (see []), Euclidean buildings (see ... See full document

... asymptotically nonexpansive mappings in the intermediate sense was introduced by Kirk 3 see also Bruck et ...asymptotically nonexpansive self-mapping in the intermediate sense has a fixed point; see ... See full document

... general iterative method for finding the solution of the variational inequality problem over the fixed point set of a nonexpansive semigroup in a Hilbert ... See full document

... Antipin, Iterative gradient prediction-type methods for computing fixed points of extremal mapping, Parametric Optimization and Related Topics, IV (Enschede, 1995) ... See full document

... Let C be a nonempty closed convex subset of a real Hilbert space H. Let F : C → H be a κ-Lipschitzian and η-strongly monotone operator with constants κ, η > 0, V, T : C → C be nonexpansive mappings with FixT / ... See full document

... A mapping T : C → C is said to be averaged non–expansive if ∀x, y ∈ C, T = (1 − β)I + βS holds for a non–expansive operator S : C → C and β ∈ (0, ...”averaged mapping” was first developed by Baillon et al ... See full document