Approximation of functions and Mihesan operators

Abstract

For real numbers \begin{document}$ a,q\geq 0 $\end{document} and a weight \begin{document}$ \varrho(x) = 1/(1+x)^q $\end{document}, the author provides necessary and sufficient conditions for a function \begin{document}$ f\in C[0,\infty) $\end{document} in order to \begin{document}$ \sup_{x\geq 0}\mid \varrho(x)(B_n^a(f,x)-f(x))\mid \to 0 $\end{document} as \begin{document}$ n\to \infty $\end{document}, where \begin{document}$ B_n^a(f) $\end{document} is the Mihesan operator. In particular, it is proved that Mihesan operators behave similar to the classical Baskakov operators.