New modification of the Post Widder operators preserving exponential functions

Abstract

AbstractThe current article deals with a modification of the Post-Widder operators which reproduce the exponential functions both [Formula: see text] and [Formula: see text] for [Formula: see text] 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
• 41A25
• 41A36
• 47A58