In this paper, we investigate the radial function manifolds generated by a linear combination of radial functions. Let Wp^r（B^d） be the usual Sobolev class of functions on the unit ball 54. We study the deviation fr...In this paper, we investigate the radial function manifolds generated by a linear combination of radial functions. Let Wp^r（B^d） be the usual Sobolev class of functions on the unit ball 54. We study the deviation from the radial function manifolds to WP^r（b^d）. Our results show that the upper and lower bounds of approximation by a linear combination of radial functions are asymptotically identical. We also find that the radial function manifolds and ridge function manifolds generated by a linear combination of ridge functions possess the same rate of approximation.展开更多
The pointwise estimates of the deviation Tn,A,Bf（·） -- f（·） in terms of moduli of continuity w. f and w. f there are proved. Analogical results on norm approximation with remarks and corollaries are also...The pointwise estimates of the deviation Tn,A,Bf（·） -- f（·） in terms of moduli of continuity w. f and w. f there are proved. Analogical results on norm approximation with remarks and corollaries are also given. In the results there are used the essentially weaker conditions than these in [Mittal, M. L.： J. Math. Anal. Appl., 220, 434-450） （1998） Theorem 1, p. 4377.展开更多
In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞）. Then we obta...In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞）. Then we obtain point-wise estimate, using the Lipschitz type maximal function.展开更多
Abstract Let {X, Xn, n ≥ 1} be a sequence of i.i.d.random variables with zero mean, and set Sn = n∑k=1Xk, EX2 = σ2 〉 0, λ（ε） = ∞∑n=1P（1Sn1 ≥ ns）. In this paper, we discuss the rate of the approximation ...Abstract Let {X, Xn, n ≥ 1} be a sequence of i.i.d.random variables with zero mean, and set Sn = n∑k=1Xk, EX2 = σ2 〉 0, λ（ε） = ∞∑n=1P（1Sn1 ≥ ns）. In this paper, we discuss the rate of the approximation of σ2 by ε2= λ（s） under suitable conditions, and improve the corresponding results of Klesov （1994）.展开更多
基金supported by the National 973 Project (Grant No. 2007CB311002)National Natural Science Foundation of China (Grant Nos. 90818020,60873206)
文摘In this paper, we investigate the radial function manifolds generated by a linear combination of radial functions. Let Wp^r（B^d） be the usual Sobolev class of functions on the unit ball 54. We study the deviation from the radial function manifolds to WP^r（b^d）. Our results show that the upper and lower bounds of approximation by a linear combination of radial functions are asymptotically identical. We also find that the radial function manifolds and ridge function manifolds generated by a linear combination of ridge functions possess the same rate of approximation.
文摘The pointwise estimates of the deviation Tn,A,Bf（·） -- f（·） in terms of moduli of continuity w. f and w. f there are proved. Analogical results on norm approximation with remarks and corollaries are also given. In the results there are used the essentially weaker conditions than these in [Mittal, M. L.： J. Math. Anal. Appl., 220, 434-450） （1998） Theorem 1, p. 4377.
文摘In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞）. Then we obtain point-wise estimate, using the Lipschitz type maximal function.
文摘Abstract Let {X, Xn, n ≥ 1} be a sequence of i.i.d.random variables with zero mean, and set Sn = n∑k=1Xk, EX2 = σ2 〉 0, λ（ε） = ∞∑n=1P（1Sn1 ≥ ns）. In this paper, we discuss the rate of the approximation of σ2 by ε2= λ（s） under suitable conditions, and improve the corresponding results of Klesov （1994）.
