Generalized blending type Bernstein operators based on the shape parameter λ
Halil Gezer, Hüseyin Aktuğlu, Erdem Baytunç, Mehmet Salih Atamert
Abstract
Abstract In the present paper, we construct a new class of operators based on new type Bézier bases with a shape parameter λ and positive parameter s . Our operators include some well-known operators, such as classical Bernstein, α -Bernstein, generalized blending type α -Bernstein and λ -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 , α , λ , and n . It should be mentioned that our operators for $\lambda =1$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> have better approximation than Bernstein and α -Bernstein operators.