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

Abstract

<p style='text-indent:20px;'>In the present paper, we consider a general class of operators enriched with some properties in order to act on <inline-formula><tex-math id="M1">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula>. We establish uniform convergence of the operators for every function in <inline-formula><tex-math id="M2">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R} _{0}^{+} $\end{document}</tex-math></inline-formula>. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.</p>