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

Mihaela Ribičić Penava
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Mihaela Ribičić Penava: Department of Mathematics, Josip Juraj Strossmayer University of Osijek, Trg Ljudevita Gaja 6, 31000 Osijek, Croatia

Mathematics, 2021, vol. 9, issue 15, 1-14

Abstract: 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 w -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.

Keywords: Hermite–Hadamard–Fejér inequalities; weighted three-point formulae; higher-order convex functions; w-harmonic sequences of functions; harmonic sequences of polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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