On a special class of modified integral operators preserving some exponential functions

Abstract

In the present paper, we consider a general class of operators enriched with some properties in order to act on \begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}. We establish uniform convergence of the operators for every function in \begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document} on \begin{document}$ \mathbb{R} _{0}^{+} $\end{document}. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.