Exponential Kantorovich-Stancu operators

Abstract

In this paper we will obtain some Bernstein-Kantorovich operators modified in Stancu sense which preserve exponential function e^μx, where μ > 0. Concerning these operators we prove they verify Korovkin’s theorem conditions and also that they approximate functions from a weighted L^p space. Moreover, we will obtain a Voronovskaya theorem and some quantitative estimates of approximation using the first order modulus of continuity. Also, we will prove some estimates concerning the approximation of functions from a weighted L^p space using Peetre’s K-functional. Finally, we will obtain an estimate which involves the first order modulus of continuity and the second order modulus of smoothness by using the equivalence relation between these moduli and the corresponding K-functionals.