Approximation by α-Bernstein-Schurer operator

Abstract

In this paper, we introduce a new family of generalized Bernstein-Schurer operators and investigate some approximation properties of these operators. We obtain a uniform approximation result using the well-known Korovkin theorem and give the degree of approximation via second modulus of smoothness. Also, we present Voronovskaya and Grüss-Voronovskaya type results for these operators.

Approximation properties of some Bernstein-Schurer type operators

“…Let 𝜑 𝑥 ∈ 𝐶 0,1 𝑝 and 0 𝜆 1, Çetin [1] constructed a generalized Bernstein-Schurer defined by 𝑉 , , 𝑓, 𝑥 ∑ 𝜑 𝑞 , 𝑥 ,…”

“…In [1], using the famous Korovkin theorem, the author studied a uniform approximation result. He also gave the rate of convergence by another modulus of smoothness.…”

On One- and Two-Dimensional α–Stancu–Schurer–Kantorovich Operators and Their Approximation Properties

“…In [30][31][32] some interesting studies have been carried out. Recently, Çetin [33] introduced a modification of Bernstein-Schurer operators introduced in (3) as:…”