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The purpose of this paper is to introduce an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a k-strict pseudo-contraction non-self mapping in Hilbert space. By the viscosity approximation algorithms, under suitable conditions , some strong convergence theorems for approximating to this common elements are proved. The results presented in the paper extend and improve some recent results of Marino and Xu [G.Marino,H.K.Xu, Weak and strong convergence theorems for k-strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336-349], Zhou [H.Zhou, Convergence theorems of fixed Points for k-strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 69 (2008) 456-462], Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506- 515], Ceng,Homidan,etc [L. C. Ceng, S.A.Homidan, Q.H.Ansari, J. C. Yao, An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings, J. Comput. Appl. Math. 223 (2009) 967-974]. [ABSTRACT FROM AUTHOR]

In this paper, we study two types of approximate solutions for a vector optimization problem in Banach space setting. Our main concern is to define two new concepts of approximate saddle points and relate them to the above solution concepts. As a result, a dual is formulated, and duality results are established. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to provide an error analysis for the multicategory support vector machine (MSVM) classificaton problems. We establish the uniform convergency approach for MSVMs and estimate the misclassification error. The main difficulty we overcome here is to bound the offset vector. As a result, we confirm that the MSVM classification algorithm with polynomial kernels is always efficient when the degree of the kernel polynomial is large enough. Finally the rate of convergence and examples are given to demonstrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of whether the best approximation to any x in a Hilbert space X from the set where C is a closed convex subset of X , S is a closed convex cone that does not necessarily have nonempty interior, Y is a Banach space, and g : X ? Y is a continuous S -convex function, can be characterized by the best approximation to a perturbation x - l of x from the set C for some l ? X . We provide a global approach to this problem by presenting a dual global constraint qualification, which is less restrictive than the Slater type (or interior-point) conditions, guaranteeing the strong conical hull intersection property (CHIP). We then show that the strong CHIP characterizes the perturbation property under a mild closure condition. The closure condition, for instance, holds whenever the explicit constraint set is described by finitely many linear inequality constraints. We also establish easily verifiable dual conditions that are equivalent to the best approximation from the set K . We finally demonstrate that our results recapture the corresponding known results in the particular case where Y is a finite dimensional space. [ABSTRACT FROM AUTHOR]