Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

Purpose of this article is to introduce a modification of Phillips operators on the interval \(\left[ \frac{1}{2},\infty \right) \) via Dunkl generalization. This type of modification enables a better error estimation on the interval \(\left[ \frac{1}{2},\infty \right) \) rather than the classical Dunkl Phillips operators on \(\left[ 0,\infty \right) \). We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's \(K\)-functional and second order modulus of continuity.