Hermite-Hadamard-type inequalities for the interval-valued approximately<i>h</i>-convex functions via generalized fractional integrals

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Zhao D., Ali M. A., Kashuri A., Budak H., Sarikaya M. Z.

JOURNAL OF INEQUALITIES AND APPLICATIONS, no.1, 2020 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Publication Date: 2020
  • Doi Number: 10.1186/s13660-020-02488-5
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Open Archive Collection: AVESIS Open Access Collection
  • Kocaeli University Affiliated: No

Abstract

In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called "interval-valued approximatelyh-convex functions". We establish some inequalities of Hermite-Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302,2018and H. Budak et al. in Proc. Am. Math. Soc.,2019). We also discussed some special cases from our main results.