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^ (x) / (x+) x λ Γ (x) / Γ (x + λ) are derived.
Koumandos et al. (Wed,) studied this question.