This paper is devoted to study direct and converse approximation theorems of the generalized Bemstein operators Cn (f, sn,x) via so-called unified modulus ωφλ^2 (f,t), 0 ≤ λ ≤1. We obtain main results as fol...This paper is devoted to study direct and converse approximation theorems of the generalized Bemstein operators Cn (f, sn,x) via so-called unified modulus ωφλ^2 (f,t), 0 ≤ λ ≤1. We obtain main results as followsωφλ^2 (f,t)=O(t^α)←→|Cn(f,sn,x)-f(x)|=O((n^-1/2δn^1-λ(x))^α),where δn^2(x)=max{φ^2(x),1/n} and 0〈α〈2.展开更多
In this paper, a simple method for merging of Bezier curves is presented by using constrained optimization method. The use of the “discrete” coefficient norm in L2 sense greatly simplifies the merging process. Furth...In this paper, a simple method for merging of Bezier curves is presented by using constrained optimization method. The use of the “discrete” coefficient norm in L2 sense greatly simplifies the merging process. Furthermore, continuity at the endpoint of curves are considered in the merging process.展开更多
基金Supported by the Natural Science Foundation of China (No. 11271263, 11371258)
文摘This paper is devoted to study direct and converse approximation theorems of the generalized Bemstein operators Cn (f, sn,x) via so-called unified modulus ωφλ^2 (f,t), 0 ≤ λ ≤1. We obtain main results as followsωφλ^2 (f,t)=O(t^α)←→|Cn(f,sn,x)-f(x)|=O((n^-1/2δn^1-λ(x))^α),where δn^2(x)=max{φ^2(x),1/n} and 0〈α〈2.
文摘In this paper, a simple method for merging of Bezier curves is presented by using constrained optimization method. The use of the “discrete” coefficient norm in L2 sense greatly simplifies the merging process. Furthermore, continuity at the endpoint of curves are considered in the merging process.