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
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）.
