On new inequalities of Hermite-Hadamard-Fejer type for harmonically convex functions via fractional integrals

Kunt M., Iscan I., Yazici N., Gözütok U.

SPRINGERPLUS, vol.5, 2016 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 5
  • Publication Date: 2016
  • Doi Number: 10.1186/s40064-016-2215-4
  • Journal Name: SPRINGERPLUS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Hermite-Hadamard inequality, Hermite-Hadamard-Fejer inequality, Riemann-Liouville fractional integrals, Harmonically convex functions
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, firstly, new Hermite-Hadamard type inequalities for harmonically convex functions in fractional integral forms are given. Secondly, Hermite-Hadamard-Fejer inequalities for harmonically convex functions in fractional integral forms are built. Finally, an integral identity and some Hermite-Hadamard-Fejer type integral inequalities for harmonically convex functions in fractional integral forms are obtained. Some results presented here provide extensions of others given in earlier works.