Generalized blending type Bernstein operators based on the shape parameter ?

Abstract

In the present paper, we construct a new class of operators based on new type Bezier bases with a shape parameter lambda and positive parameter s. Our operators include some well-known operators, such as classical Bernstein, alpha-Bernstein, generalized blending type alpha-Bernstein and lambda-Bernstein operators as special case. In this paper, we prove some approximation theorems for these operators. Approximation properties of our operators are illustrated on graphs for variables s, alpha, lambda, and n. It should be mentioned that our operators for lambda = 1 have better approximation than Bernstein and alpha-Bernstein operators.