Approximation by $\alpha$-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.

Keywords

• Bernstein-Schurer operators
• α-Bernstein operator
• Modulus of continuity
• Voronovskaya type theorem
• Grüss-Voronovskaya type theorem

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