A note on Stancu operators with three parameters

Abstract

In this paper, we consider the sequence of positive linear operators L^α,β_n,r depending on three non-negative parameters; an integer r and two reals α and β such that α ≤ β, constructed by Stancu. We consider a Kantorovich-type generalization of Stancu’s operators and investigate their convergence properties in Lp-norm. Finally, we observe variation detracting property for the Stancu operator and its Kantorovich modification. Moreover, we show that the Stancu operator satisfies an inequality that we call variation detracting when the attached function is of bounded p-variation in the sense of Riesz.