Convergence of derivative of Szász type operators involving Charlier polynomials

Abstract

<p style='text-indent:20px;'>The paper deals with the approximation of first order derivative of a function by the first order derivative of Szász-type operators based on Charlier polynomials introduced by Varma and Taşdelen [<xref ref-type="bibr" rid="b20">20</xref>]. The uniform convergence theorem, Voronovskaja type asymptotic theorem and an estimate of error in terms of the second order modulus of continuity of the derivative of the function are investigated. Further, it is shown that linear combinations of the derivative of the above operators converge to the derivative of function at a faster rate. Finally, an estimate of error in the approximation is obtained in terms of the <inline-formula><tex-math id="M1">\begin{document}$ (2k+2)th $\end{document}</tex-math></inline-formula> order modulus of continuity using Steklov mean.</p>