Post-quantum Hermite-Hadamard type inequalities for interval-valued convex functions

Ali M. A., Budak H., Murtaza G., Chu Y.

JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2021, no.1, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1186/s13660-021-02619-6
  • 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
  • Kocaeli University Affiliated: No

Abstract

In this research, we introduce the notions of (p, q)-derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite-Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite-Hadamard type. It is also shown that the results proved in this study are the generalization of some already proved research in the field of Hermite-Hadamard inequalities.