APPROXIMATION PROPERTIES FOR DIFFERENCE OF POSITIVE LINEAR OPERATORS

Abstract

In the present paper, we deal with the general quantitative estimates for the differences of recently defined composition positive linear operators (p.l.o.) by Gupta with the most representative operators used in approximation theory. The differences of these composition operators with various other available composition operators and Sz\'{a}sz operators of Durrmeyer type have been studied.
%i.e. Sz\'{a}sz-Durrmeyer type operators.
The estimates for the differences of operators having:
\begin{itemize}
\item different basis functions but same functional

\item different basis functions and different functionals

\item same basis function but different functionals

\end{itemize}
are calculated. Further the theoretical results are verified using numerical examples. Moreover the quantitative estimates in terms of weighted modulus of continuity have also been discussed.\\
\textbf{Keywords:} modulus of continuity, weighted modulus, composition operators, difference of operators, approximation operators.