Affiliation:
1. Department of Mathematics and Informatics Lucian Blaga University of Sibiu Sibiu Romania
2. Faculty of Science, Department of Mathematics Gazi University Ankara Turkey
Abstract
We introduce a new representation of recently introduced perturbed Bernstein operators
in terms of classical Bernstein operators. Using this new representation, we investigate the shape‐preserving properties of the operator
. In particular, we prove that perturbed Bernstein operators preserve monotonicity and convexity of functions for certain cases. On the other hand, we demonstrate with some counterexamples that monotonicity and convexity preserving properties fail in other cases. Moreover, we present some weaker results in these cases.
Subject
General Engineering,General Mathematics