Approximation degree of Durrmeyer–Bézier type operators

Abstract

Recently, a mixed hybrid operator, generalizing the well-known Phillips operators and Baskakov–Szász type operators, was introduced. In this paper, we study Bézier variant of these new operators. We investigate the degree of approximation of these operators by means of the Lipschitz class function, the modulus of continuity, and a weighted space. We study a direct approximation theorem by means of the unified Ditzian–Totik modulus of smoothness. Furthermore, the rate of convergence for functions having derivatives of bounded variation is discussed.

On the Bézier Variant of the Srivastava-Gupta Operators

“…In 2007, Guo et al [15] studied Baskakov-Bézier operators and established direct, inverse and equivalence approximation theorems with the help of Ditzian-Totik modulus of smoothness. Very recently, Agrawal et al [5] introduced mixed hybrid operators for which they got direct results and the rate of convergence for differentiable functions whose derivatives are of bounded variation. Many other interesting Bézier type operators were studied by several researchers, cf.…”

Rate of convergence of Gupta-Srivastava operators based on certain parameters

“…Many authors have already discussed weighted modulus of continuity for various linear positive operators. For more information (see [2], [3], [5]).…”

Bézier variant of the Szász-Durrmeyer type operators based on the Poisson-Charlier polynomials

“…In 2007, Guo et al [9] studied Baskakov-Bézier operators and established direct, inverse and equivalence approximation theorems with the help of Ditzian-Totik modulus of smoothness. Very recently, Agrawal et al [3] introduced mixed hybrid operators for which they got direct results and the rate of convergence for differential functions whose derivatives are of bounded variation. Many other interesting Bézier type operators were studied by several researchers, and the reader is invited to see [1], [2], [4], [6], [8], [10], [13], [15], [16], [17], [21], [22].…”