On the Parametric Approximation Results of Phillips Operators Involving the q-Appell Polynomials

The motive of the present paper is to construct q-Phillips operators generated by the parametric extension of exponential function by including the parameter ζ∈[-12,∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta \in \big [ -\frac{1}{2}, \infty )$$\end{document}. First we give the basic estimates to obtain their central moments and then study the Korovkin’s-type approximation theorems. Moreover, we investigate local approximation results via Peetre’s K-functional, modulus of continuity and Lipschitz-type approximation.