On integral generalization of Lupaş-Jain Operators

Abstract

This paper mainly is a natural continuation of ?On Lupa?-Jain Operators? constructed by Ba?canbaz-Tunca et al. (Stud. Univ. Babe?-Bolyai Math. 63(4) (2018), 525-537) to approximate integrable functions on [0;1). We first present the weighted uniform approximation and provide a quantitative estimate for integral generalization of Lupa?-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.