Szász–Mirakyan Type Operators Which Fix Exponentials

Abstract

In this paper, we construct a new general class of operators which have the classical Szasz Mirakyan ones as a basis, and fix the functions \(e^{ax}\) and \(e^{2ax}\) with \(a>0\). The convergence of the corresponding sequences is discussed in exponential weighted spaces, and a Voronovskaya type result is given. Also we define a new weighted modulus of smoothness and determine the approximation order of the constructed operators. Finally, we study the goodness of the estimates of our new operators via saturation results.