A note on the convergence of Phillips operators by the sequence of functions via q-calculus

Abstract

The basic aim of this study is to include nonnegative real parameters to allow for approximation findings of the Stancu variant of Phillips operators. We concentrate on the uniform modulus of smoothness in a simple manner before moving on to the approximation in weighted Korovkin’s space. Our study’s goals and outcomes are to fully develop the uniformly approximated findings of Phillips operators. We determine the order of convergence in terms of Lipschitz maximal function and Peetre’s K-functional. In addition, the Voronovskaja-type theorem is also proved.

Keywords

• szász operator
• q-integers
• exponential generating functions
• dunkl analogue
• modulus of continuity
• 41a25
• 41a36
• 33c45