Quantum Hermite-Hadamard-type inequalities for functions with convex absolute values of second q<SUP>b</SUP>-derivatives

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Ali M. A., Budak H., Abbas M., Chu Y.

ADVANCES IN DIFFERENCE EQUATIONS, no.1, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1186/s13662-020-03163-1
  • Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Kocaeli University Affiliated: No

Abstract

In this paper, we obtain Hermite-Hadamard-type inequalities of convex functions by applying the notion of qb-integral. We prove some new inequalities related with right-hand sides of qb-Hermite-Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite-Hadamard inequalities.