A note on ( p , q ) $(p,q)$ -Bernstein polynomials and their applications based on ( p , q ) $(p,q)$ -calculus

A NOTE ON THE (p; q)-HERMITE POLYNOMIALS

In this paper, we introduce a new generalization of the Hermite polynomials via (p; q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, explicit formula, recurrence relation, integral representation. We also de…ne a (p; q)analogue of the Bernstein polynomials and acquire their some formulas. We then provide...

A Note on the Modified q-Bernstein Polynomials

A de Casteljau Algorithm for Bernstein type Polynomials based on (p, q)-integers in CAGD

In this paper, a de Casteljau algorithm to compute (p, q)-Bernstein Bézier curves based on (p, q)integers is introduced. We study the nature of degree elevation and degree reduction for (p, q)-Bézier Bernstein functions. The new curves have some properties similar to q-Bézier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain (u, v) ∈ [0, 1]× [0...

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, p...

SOME APPROXIMATION RESULTS FOR BERNSTEIN-KANTOROVICH OPERATORS BASED ON (p, q)-CALCULUS

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...