NEW PROOFS OF FEJER’S AND DISCRETE HERMITE-HADAMARD INEQUALITIES WITH APPLICATIONS

SEKİN Ç., TAMAR M. E., Aliyev I. A.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol.72, no.4, pp.1110-1125, 2023 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.31801/cfsuasmas.1262668
  • Journal Name: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1110-1125
  • Keywords: convex functions, discrete Hermite-Hadamard inequality, Fejer inequality, Hardy inequality, Jensen inequality
  • Abdullah Gül University Affiliated: Yes

Abstract

New proofs of the classical Fejer inequality and discrete Hermite-Hadamard inequality (HH) are presented and several applications are given, including (HH)-type inequalities for the functions, whose derivatives have inflection points. Morever, some estimates from below and above for the first moments of functions f: [a, b] → R about the midpoint c = (a+b)/2 are obtained and the reverse Hardy inequality for convex functions f: (0, ∞) → (0, ∞) is established.