On Baskakov operators preserving the exponential function

Abstract

In this paper, we are concerned about the King-type Baskakov operators defined by means of the preserving functions \(e_{0}\) and \(e^{2ax},\ a>0\) fixed. Using the modulus of continuity, we show the uniform convergence of new operators to \(f\). Also, by analyzing the asymptotic behavior of King-type operators with a Voronovskaya-type theorem, we establish shape preserving properties using the generalized convexity.

Keywords

• Baskakov operators
• King type operators
• Voronovskaya type theorems
• modulus of continuity