[PDF] Top 20 On solving the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings

... a point x to a subset ...a multivalued mapping. An element x ∈ C is called a fixed point of S if x ∈ ...a multivalued mapping S : C → CB(C) is ... See full document

... Theorem 3.2. Let E be a strictly convex reflexive Banach space having the Kadec-Klee property and a Fr´echet differentiable norm, C a nonempty closed convex subset of E, A : C → E ∗ a continuous and monotone mapping, ψ : ... See full document

... the generalized equilibrium problem (GEP) using the KKM mapping in a Banach space ...the fixed point set of countable family of nonexpansive mappings in the ... See full document

... We note that -hybrid is nonexpansive, -hybrid is nonspreading, and if S is λ-hybrid with F(S) = ∅ , then S is quasi-nonexpansive. It is well known [] that if S is λ-hybrid, then F(S) is closed. In ... See full document

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

... the equilibrium problems (.) and (.), the fixed point problem for a family of infinitely nonexpansive mappings, and the problem of zero points of maximal monotone ... See full document

... finite family of generalized nonexpansive multivalued mappings and the solution set of two equilibrium problems in a Hilbert space is ... See full document

... common fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem, and the solution set of the classical variational inequality problem for a monotone ... See full document

... a generalized equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert ... See full document

... Let H be a real Hilbert space with inner product h., .i and norm || · ||, and let K be a nonempty closed convex subset of H. Let B : K → H be a nonlinear mapping, ϕ : K → R ∪ {+∞} be a function and F : K ×K → R , be a ... See full document

... for fixed point problems and variational inequality problems,” Journal of Inequalities and Applications, ...a generalized equilibrium problem with a relaxed monotone mapping and a ... See full document

... fixed point method de- fined by ...mixed equilibrium problem and common fixed point problems of a countable family of multivalued nonexpansive mappings in ... See full document

... Theorem 3.3. Let E be a nonempty closed convex bounded subset of a uniformly convex Banach space X. Let t : E → E be a single-valued mapping, and let T : E → KCE be a multivalued mapping. If both t and T satisfy ... See full document

... That is, x ∗ solves the SFP (.) if and only if x ∗ solves the fixed point equation (.) (see [] for the details). This implies that we can use fixed point algorithms (see [, –]) to solve SFP. A ... See full document

... 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

... Definition . Let E be a smooth, strictly convex and reflexive Banach space, and K be a nonempty, closed and convex subset of E. Let S : K → K be a nonlinear mapping with F(S) being a nonempty closed and convex subset of ... See full document

... Theorem 4 Let C be a nonempty closed convex and bounded subset of a real Hilbert space H. Let f : C → C be ρ -contraction mapping, A be an α -inverse strongly monotone mapping of C into H, and T : C → C be asymptotically ... See full document

... Theorem . ([]) Let C be a nonempty, bounded, closed and convex subset of a real Hilbert space H and let ϕ : C → R be a lower semicontinuous and convex functional. Let T : C → CB(H) be H-Lipschitz continuous with ... See full document

... Takahashi, “Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces,” Journal of Mathematical Analysis and Applications , vol. Wong, “Viscosit[r] ... See full document

... the split common fixed point problem of quasi-nonexpansive map- pings in Hilbert ...a split common fixed point of other nonlinear mappings, such as nonspreading type ... See full document