Approximations of generalized Bernstein functions

Abstract

We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a related function, namely $x^{\hat{I}}»\hat{I}“(x)/\hat{I}“(x+\hat{I}»)$ are derived.

19 pages