New modification of the Post Widder operators preserving exponential functions

Abstract

The current article deals with a modification of the Post-Widder operators which reproduce the exponential functions both $e^{\mu x}$ and $e^{2\mu x}$ for $\mu >0.$ The central moments, uniform convergence of the operators and the rate of convergence of these operators with the help of modulus of continuity are estimated. Also, a Voronovskaja-type asymptotic formula is established. After that, numerical results are obtained to confirm the theoretical results. Finally, new constructed operators are compared with modified Post-Widder operators.

Keywords:

• Post-Widder operators
• exponential functions
• Voronovskaya-type theorem

MSC CLASSIFICATION:

• 41A25
• 41A36
• 47A58

Disclosure statement

No potential conflict of interest was reported by the authors.