A New Family of Szász–Mirakyan-Type Operators Preserving Two Exponential Functions

This paper introduces a new family of Szász–Mirakyan-type operators defined by a convex combination of two Poisson-type constructions. The operators preserve the constant function and provide a continuous transition between different exponential behaviors through a parameter sequence. Basic properties of the operators are studied, including the preservation of exponential test functions and the behavior of the first and second central moments. Voronovskaja-type asymptotic results are obtained, describing the effect of the parameter on the asymptotic structure. Moreover, a necessary condition for faster-than 1/n approximation is derived. The behavior of the operators is examined through computational evidence, which also confirms the theoretical findings.