Characterization Theorems for the Approximation by a Family of Operators (original) (raw)

On approximation by a class of new Bernstein type operators

Applied Mathematics and Computation, 2008

This paper is concerned with a new type of the classical Bernstein operators where the function is evaluated at intervals ½0; 1 À 1 nþ1 . We also make extensive study simultaneous approximation by the linear combination L n ðf ; k; xÞ of these new Bernstein type operators L n ðf Þ. At the end of this paper we have given an other modification of these operators.

Approximation theorems for certain positive linear operators

Applied Mathematics Letters, 2010

In this work we prove approximation theorems for certain positive linear operators via Ditzian-Totik moduli ω 2,φ (f , •) of second order where the step-weights are functions whose squares are concave. The results obtained are applied to the q-Lupaş-Bernstein operators, the ω, q-Bernstein operators and the convergence of the iterates of the q-Bernstein polynomials.

On some constants in approximation by Bernstein operators

We estimate the constants sup x∈(0,1) sup f ∈C[0,1]\Π 1 |Bn(f,x)−f (x)| ω 2 f, Õ x(1−x) n and inf x∈(0,1) sup f ∈C[0,1]\Π 1 |Bn(f,x)−f (x)| ω 2 f, Õ x(1−x) n , where B n is the Bernstein operator of degree n and ω 2 is the second order modulus of continuity.

On Approximation Properties of (p,q)-Bernstein Operators

European Journal of Pure and Applied Mathematics

In this study, a (p,q)-analogue of Bernstein operators is introducedand approximation properties of (p,q)-Bernstein operators areinvestigated. Some basic theorems are proved. The rate of approximationby modulus of continuity is estimated.

Some approximation properties of ( p , q ) (p,q)(p,q)(p,q) -Bernstein operators

Journal of Inequalities and Applications, 2016

This paper is concerned with the (p, q)-analog of Bernstein operators. It is proved that, when the function is convex, the (p, q)-Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that verify these properties are considered. A global approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem are proved.

Better approximation results by Bernstein–Kantorovich operators

Lobachevskii Journal of Mathematics, 2017

In this paper, we give a King-type modification of the Bernstein-Kantorovich operators and study the approximation properties of these operators. We prove that the error estimation of these operators is better than the classical Bernstein-Kantorovich operators. We also give some estimations for the rate of convergence of these operators by using the modulus of continuity. Furthermore, we obtain a Voronovskaya-type asymptotic formula for these operators.