Convergence of iterates of q-Bernstein and (p,q)-Bernstein operators and the Kelisky-Rivlin type theorem

Abstract

Recently, Radu [Note on the iterates of q and (p,q)-Bernstein operators, Scientific Studies and Research, Series Mathematics and Informatics, 26(2) (2016) 83-94] has investigated the convergence of iterates of q-Bernstein polynomial and (p,q)-Bernstein polynomial with the aids of weakly Picard operators theory. In this article, we establish Kelisky-Rivlin type theorem on the power of the q-Bernstein operators for two dimensional case, (p,q)-Bernstein operators and bivariate (p,q)-Bernstein operators by using contraction principle.