This paper is aimed at studying sensitivity of parameters α and β appearing in the operators introduced by D.D. Stancu [11] in 1969. Results are established on the behavior the nodes used in Bernstein-Stancu polynomials and the nodes used in Bernstein polynomials and graphical presentations of them are generated. Alternate proof of uniform convergence of Bernstein-Stancu operators and an upper ...

Abstract In the present paper, we construct a new class of operators based on type Bézier bases with shape parameter λ and positive s . Our include some well-known operators, such as classical Bernstein, α -Bernstein, generalized blending -Bernstein special case. this prove approximation theorems for these operators. Approximation properties our are illustrated graphs variables , n It should be...

In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators sequence are determined on the Wiener space.

"A new class of Bernstein-type operators are obtained by applying an iterative method modi cations starting from the Bernstein operators. These have good properties approximation functions and their derivatives."

The Bernstein operators allow to build recursively the Schur functions. We present a recursion formula for k-Schur functions at t = 1 based on combinatorial operators that generalize the Bernstein operators. The recursion leads immediately to a combinatorial interpretation for the expansion coefficients of k-Schur functions at t = 1 in terms of homogeneous symmetric functions.

In this paper, a new analogue of Bernstein-Kantorovich operators as (p, q)-Bernstein-Kantorovich operators are introduced. We discuss approximation properties for these operators based on Korovkin’s type approximation theorem and we compute the order of convergence using usual modulus of continuity and also the rate of convergence when the function f belongs to the class LipM (α). Moreover, the...

In this paper we discuss convergence properties and error estimates of rational Bernstein operators introduced by P. Piţul and P. Sablonnière. It is shown that the rational Bernstein operators converge to the identity operator if and only if the maximal difference between two consecutive nodes is converging to zero. Further a Voronovskaja theorem is given based on the explicit computation of hi...

In the present note, we introduce a Bezier variant of a new type of Bernstein Durrmeyer operator, which was introduced by Gupta [3]. We estimate the rate of convergence by using the decomposition technique of functions of bounded variation and applying the optimum bound. It is observed that the analysis for our Bezier variant of new Bernstein Durrmeyer operators is different from the usual Bern...