Hermite–Hadamard–Fejér-Type Inequalities and Weighted Three-Point Quadrature Formulae

• Main Author: Mihaela Ribičić Penava
• Format: Article
• Language: English
• Published: MDPI AG 2021-07-01
• Series: Mathematics
• Subjects: Hermite–Hadamard–Fejér inequalities; weighted three-point formulae; higher-order convex functions; w-harmonic sequences of functions; harmonic sequences of polynomials
• Online Access: https://www.mdpi.com/2227-7390/9/15/1720
• ISSN: 2227-7390

The goal of this paper is to derive Hermite–Hadamard–Fejér-type inequalities for higher-order convex functions and a general three-point integral formula involving harmonic sequences of polynomials and <i>w</i>-harmonic sequences of functions. In special cases, Hermite–Hadamard–Fejér-type estimates are derived for various classical quadrature formulae such as the Gauss–Legendre three-point quadrature formula and the Gauss–Chebyshev three-point quadrature formula of the first and of the second kind.