On the convergence of Lupaş ( p , q ) $(p,q)$ -Bernstein operators via contraction principle

On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators

In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...

Convergence of rational Bernstein operators

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...

Modified (p,q)-Bernstein-Schurer operators and their approximation properties

On the Convergence and Iterates of q-Bernstein Polynomials

The convergence properties of q-Bernstein polynomials are investigated. When q > 1 is fixed the generalized Bernstein polynomials Bnf of f , a one parameter family of Bernstein polynomials, converge to f as n → ∞ if f is a polynomial. It is proved that, if the parameter 0 < q < 1 is fixed, then Bnf → f if and only if f is linear. The iterates of Bnf are also considered. It is shown that B n f c...

Approximation Results For q-Parametric BBH Operators

The paper introduces q-parametric Bleimann, Butzer and Hahn (q-BBH) operators as a rational transformation of q-Bernstein-Lupaş operators. On their basis, a set of new results on q-BBH operators can be obtained easily from the corresponding properties of q-Bernstein-Lupaş operators. Furthermore, convergence properties of q-BBH operators are studied.