Approximations of generalized Bernstein functions

2024/09/04 by Koumandos, Stamatis, Pedersen, Henrik Laurberg
#44A10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.02536

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^λΓ(x)/Γ(x+λ) are derived.

Related

• Higher order Thorin-Bernstein Functions
• Some two-parameter families of generalized Bernstein functions
• (p,q)-Beta Functions and Applications in Approximation
• A Bernstein type inequality
• Another weighted approximation of functions with singularities by combinations of Bernstein operators