On Integral Generalization of Lupas-Jain Operators

Abstract

This paper mainly is a natural continuation of "On Lupas-Jain Operators" constructed by  Bascanbaz-Tunca et al. (Stud. Univ. Babe\c{s}-Bolyai Math. 63(4) (2018), 525-537) to approximate integrable functions on [0,\infty). We first present the weighted uniform approximation and provide a quantitative estimate for integral generalization of Lupas-Jain operators. We also scrutinize the order of approximation in regards to local approximation results in sense of a classical approach, Peetre's K-functional and Lipschitz class. Then, we prove that given operators can be approximated in terms of the Steklov means (Steklov averages). Lastly, a Voronovskaya-type asymptotic theorem is given.