Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore,...Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore, the Busemann-Petty type problem for L_p mixed intersection bodies are shown.展开更多
In this paper,the L_p-convergence of Grünwald interpolation G_n(f,x)based on the zeros of Jacobi polynomials J^((α,β))_n(x)(-1<α,β<1)is considered.L_p-convergence(0<p<2) of Grünwald interpola...In this paper,the L_p-convergence of Grünwald interpolation G_n(f,x)based on the zeros of Jacobi polynomials J^((α,β))_n(x)(-1<α,β<1)is considered.L_p-convergence(0<p<2) of Grünwald interpolation G_n(f,x)is proved for p·Max(α,β)<1.Moreover, L_p-convergence(p>0)of G_n(f,x)is obtained for-1<α,β≤0.Therefore,the results of [1]and [3-5]are improved.展开更多
The degree of approximation to a function f(x)∈C[-1,1] by (U, λ) means and f(x) ∈ Lpw by (Jr) means are discussed, some results in the literatures [1],[2],[3] have been improved.
Some new characterizations and immediate explicit expressions of best L(1≤p≤∞) approximation and their deviations by an n-dimensional subspace on a set of n+1 points are given.
The purpose of the present paper is to evaluate the error of the approximation of the func- tion fL_1[0,1]by Kantorovich-Bernstein polynomials in L_p-metric(0<p<1).
基金Supported by the Natural Science Foundation of Hunan Province（2017JJ3085＋16C0635） Supported by the China Postdoctoral Science Foundation（2016M601644）
文摘Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore, the Busemann-Petty type problem for L_p mixed intersection bodies are shown.
文摘In this paper,the L_p-convergence of Grünwald interpolation G_n(f,x)based on the zeros of Jacobi polynomials J^((α,β))_n(x)(-1<α,β<1)is considered.L_p-convergence(0<p<2) of Grünwald interpolation G_n(f,x)is proved for p·Max(α,β)<1.Moreover, L_p-convergence(p>0)of G_n(f,x)is obtained for-1<α,β≤0.Therefore,the results of [1]and [3-5]are improved.
文摘The degree of approximation to a function f(x)∈C[-1,1] by (U, λ) means and f(x) ∈ Lpw by (Jr) means are discussed, some results in the literatures [1],[2],[3] have been improved.
文摘Some new characterizations and immediate explicit expressions of best L(1≤p≤∞) approximation and their deviations by an n-dimensional subspace on a set of n+1 points are given.
文摘The purpose of the present paper is to evaluate the error of the approximation of the func- tion fL_1[0,1]by Kantorovich-Bernstein polynomials in L_p-metric(0<p<1).
