Reconstruction of Sza´sz-Mirakyan operators preserving exponential type functions

Abstract

In this paper, we construct a modification of Sza´sz-Mirakyan operators with a new technique that preserved the exponential functions i.e. exp(µt) and exp(2µt), µ > 0. We study the asymptotic behaviour and  weighted approximation of these operators. Comparisons about one approximate better between the recent operators and the classical Sza´sz-Mirakyan operators have also been presented. In the end, we compare the convergence of these operators and modified Baskakov operators to  certainf by illustrative graphics using the Mathematica algorithms.
Keywords: Szasz operators, rate of convergence, degree of approximation, approximation by positive operators.
Mathematics Subject Classification(2010): 41A25, 26A15, 41A30, 41A36.