The aim of this paper is to solve the fixed point problems : v = Ov, with Ov(x) def = max(Lv(x), Bv(x)), x ∈ E , (1) where E is a finite set, L is contractive and B is a nonexpansive operator and v = Ov, with Ov(x) def = max(sup w Lv(x), sup z Bv(x)), x ∈ E , (2) where W and Z are general control sets, the operators L are contractive and operators B are nonexpansive. For these two problems, we ...

Let H be a real Hilbert space. Consider on H a nonexpansive semigroup S {T s : 0 ≤ s < ∞} with a common fixed point, a contraction f with the coefficient 0 < α < 1, and a strongly positive linear bounded self-adjoint operator A with the coefficient γ > 0. Let 0 < γ < γ/α. It is proved that the sequence {xn} generated by the iterative method x0 ∈ H, xn 1 αnγf xn βnxn 1 − βn I − αnA 1/sn ∫sn 0 T ...

In this paper, we introduce and analyze some generalized hybrid proximal point algorithms for finding a common element of the set of zeros of a maximal monotone operator and the set of fixed points of a nonexpansive mapping in a Hilbert space. These algorithms include the previously known proximal point algorithms as special cases. Weak and strong convergence of the proposed proximal point algo...

The main strategy of this paper is intended to speed up the convergence inertial Mann iterative method and further it through normal S-iterative for a certain class nonexpansive-type operators that are linked with variational inequality problems. Our new theory permits us settle down difficulty unification Korpelevich’s extragradient method, Tseng’s extragardient subgardient solving problems an...

Let (Ω,Σ) be a measurable space, with Σ a sigma-algebra of subset of Ω, and let C be a nonempty bounded closed convex separable subset of a Banach space X , whose characteristic of noncompact convexity is less than 1, KC(X) the family of all compact convex subsets of X . We prove that a multivalued nonexpansive non-self-random operator T :Ω×C → KC(X), 1-χ-contractive mapping, satisfying an inwa...

Let H be a real Hilbert space and S = {T (s) : 0 ≤ s < ∞} be a nonexpansive semigroup on H such that F (S) 6= ∅. For a contraction f with coefficient 0 < α < 1, a strongly positive bounded linear operator A with coefficient γ̄ > 0. Let 0 < γ < γ̄ α . It is proved that the sequences {xt} and {xn} generated by the iterative method xt = tγf(xt) + (I − tA) 1 λt ∫ λt

Network bandwidth allocation is a central issue in modern communication networks. The main objective of the bandwidth allocation is to allocate an optimal bandwidth for maximizing a predefined utility over the capacity constraints to traffic sources. When a centralized operator, which manages all the bandwidth allocations in the network, has a certain operational policy, the bandwidth allocatio...

In this paper, we prove the existence of a random common fixed point of two continuous contractive random operators on a separable Banach space. We introduce the random modified Ishikawa iteration scheme and use our existence result to study weak and strong convergence of this scheme to a unique random common fixed point of two random asymptotically quasi-nonexpansive operator. Our work extends...

We introduce new general iterative approximation methods for finding a common fixed point of a countable family of nonexpansive mappings. Strong convergence theorems are established in the framework of reflexive Banach spaces which admit a weakly continuous duality mapping. Finally, we apply our results to solve the the equilibrium problems and the problem of finding a zero of an accretive oper...

Finding a fixed point to a nonexpansive operator, i.e., x∗ = Tx∗, abstracts many problems in numerical linear algebra, optimization, and other areas of scientific computing. To solve fixed-point problems, we propose ARock, an algorithmic framework in which multiple agents (machines, processors, or cores) update x in an asynchronous parallel fashion. Asynchrony is crucial to parallel computing s...