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In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm L p (1 ≤ p ≤ ∞) of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results. [ABSTRACT FROM AUTHOR]

In this paper we study zero-sum stochastic games. The optimality criterion is the long-run expected average criterion, and the payoff function may have neither upper nor lower bounds. We give a new set of conditions for the existence of a value and a pair of optimal stationary strategies. Our conditions are slightly weaker than those in the previous literature, and some new sufficient conditions for the existence of a pair of optimal stationary strategies are imposed on the primitive data of the model. Our results are illustrated with a queueing system, for which our conditions are satisfied but some of the conditions in some previous literatures fail to hold. [ABSTRACT FROM AUTHOR]

Letbe a unit sphere of thed-dimensional Euclidean space Rd and let(0 < p= 1) denote the real Hardy space onFor 0 < p= 1 andletEj(f,Hp) (j= 0, 1, ...) be the best approximation offby spherical polynomials of degree less than or equal toj, in the spaceGiven a distributionfonits Cesàro mean of order d>-1 is denoted byFor 0p. In this paper, the following result is proved:TheoremLet0N(f)˜BN(f)means that there’s a positive constant C, independent of N and f, such thatIn the cased= 2,this result was proved by Belinskii in 1996. [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 investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give some direct and inverse results on pointwise simultaneous approximation by the combinations of Baskakov operators. We also give a new equivalent result on pointwise approximation by these operators. [ABSTRACT FROM AUTHOR]

The study of zeros of orthogonal functions is an important topic. In this paper, by improving the middle variable x(t), we've got a new form of asymptotic approximation, completed with error bounds, it is constructed for the Jacobi functions ϕμ(αβ) (t) (α > -1) as μ → + ∞. Besides, an accurate approximation with error bounds is also constructed correspondingly for the zeros tμ,8 of ϕμ(αβ) (t) (α ≥ -0) as μ → + ∞, uniformly with respect to s = 1,2,.... [ABSTRACT FROM AUTHOR]

We investigate two classes of orthonormal bases for L2([0, 1) n). The exponential parts of those bases are multi-knot piecewise linear functions which are called spectral sequences. We characterize the multi-knot piecewise linear spectral sequences and give an application of the first class of piecewise linear spectral sequences. [ABSTRACT FROM AUTHOR]