Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators

Abstract

Abstract In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also considered. Finally, the Voronovskaya type theorem is demonstrated for some particular case of these polynomials.

Keywords

• Szasz operators
• Brenke type polynomials
• Jakimovski–Leviatan operators
• Modulus of continuity
• Weighted space