Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces

The purpose of this paper is to study the robustness of Mann type algorithm in the sense that approximately perturbed mapping does not alter the convergence of Mann type algorithm. It is proven that Mann type algorithm with perturbed mapping xn+1=λnxn+(1−λn)(Txn+en)−λnμnF(xn) remains convergent in a Banach space setting where λn,μn∈[0,1], T a nonexpansive mapping, en, n=0,1,…, errors and F a strongly accretive and strictly pseudocontractive mapping

Hybrid Approximate Proximal Method with Auxiliary Variational Inequality for Vector Optimization

This paper studies the general vector optimization problem of finding weakly efficient points for mappings in a Banach space Y, with respect to the partial order induced by a closed, convex, and pointed cone C C Y with nonempty interior. In order to find a solution of this problem, we introduce an auxiliary variational inequality problem for monotone, Lipschitz-continuous mapping. The approximate proximal method in vector optimization is extended to develop a hybrid approximate proximal method for the general vector optimization problem by the combination of extragradient method for finding a solution to the variational inequality problem and approximate proximal point method for finding a root of a maximal monotone operator. In this hybrid approximate proximal method, the subproblems consist of finding approximate solutions to the variational inequality problem for monotone, Lipschitz-continuous mapping, and finding weakly efficient points for suitable regularizations of the original mapping. We present both an absolute and a relative version in which the subproblems are solved only approximately. Weak convergence of the generated sequence to a weak efficient point is established under quite mild conditions. In addition, we also discuss an extension to Bregman-function-based hybrid approximate proximal algorithms for finding weakly efficient points for mappings

Implicit Iterative Method for Hierarchical Variational Inequalities

We introduce a new implicit iterative scheme with perturbation for finding the approximate solutions of a hierarchical variational inequality, that is, a variational inequality over the common fixed point set of a finite family of nonexpansive mappings. We establish some convergence theorems for the sequence generated by the proposed implicit iterative scheme. In particular, necessary and sufficient conditions for the strong convergence of the sequence are obtained

Hybrid and Relaxed Mann Iterations for General Systems of Variational Inequalities and Nonexpansive Mappings

We introduce hybrid and relaxed Mann iteration methods for a general system of variational inequalities with solutions being also common solutions of a countable family of variational inequalities and common fixed points of a countable family of nonexpansive mappings in real smooth and uniformly convex Banach spaces. Here, the hybrid and relaxed Mann iteration methods are based on Korpelevich’s extragradient method, viscosity approximation method, and Mann iteration method. Under suitable assumptions, we derive some strong convergence theorems for hybrid and relaxed Mann iteration algorithms not only in the setting of uniformly convex and 2-uniformly smooth Banach space but also in a uniformly convex Banach space having a uniformly Gateaux differentiable norm. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature

Rare B -> K^* l^+ l^- Decay in Light Cone QCD

We investigate the transition formfactors for the B -> K^* l^+ l^- (l = mu, tau) decay in the light cone QCD. It is found that the light cone and 3-point QCD sum rules analyses for some of the formfactors for the decay B -> K^* l^+ l^- lead to absolutely different $q^2$ dependence. The invariant dilepton mass distributions for the B -> K^* mu^+ mu^- and B -> K^* tau^+ tau^- decays and final lepton longitudinal polarization asymmetry, which includes both short and long-distance contributions, are also calculated.Comment: 19 pages, 5 figures, LaTeX formatted. METU-PHYS-HEP-96-3