Pointwise weighted approximation of functions with endpoint singularities by combinations of Bernstein operators

Pointwise weighted approximation of functions with inner singularities by Bernstein operators

We consider the pointwise weighted approximation by Bernstein operators with inner singularities. The related weight functions are weights $\bar{w}(x)=|x-ξ|^α(0<ξ<1,\ α>0).$ In this paper we give direct and inverse results of this type of Bernstein polynomials.

Pointwise Approximation Theorems for Combinations of Bernstein Polynomials With Inner Singularities

We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.

Direct and Inverse Estimates for Combinations of Bernstein Polynomials with Endpoint Singularities

We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein polynomials by the $r$th Ditzian-Totik modulus of smoothness $ω_ϕ^{r}(f,t)_w$ where $ϕ$ is an admissible step-weight function.

Pointwise weighted approximation of functions with inner singularities by combinations of Bernstein operators

We introduce another new type of combinations of Bernstein operators in this paper, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type combinations are obtained.

Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus

We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the $q$-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in $]0,1[$. Numerous properties of the modified Bernstein Polynomials are extended to their $q$-analogues: simultaneous approximation, pointwise convergence even for unbounded functions, shape-preserving property, Voronovskaya theorem, self-adjointness. Some properties of the eigenvectors, which are $q$-extensions of Jacobi polynomi…

关于积分核算子的最优端点

On optimal endpoints for integral kernel operators

研究单变量函数上积分核算子行为，在重排不变拟范数赋范的巴拿赫空间类中找最优端点空间候选者，刻画非增重排具体逐点估计的存在性并构建理论，以此为一些积分核算子提出最优端点空间。