New Quantum Hermite-Hadamard-Type Inequalities for <i>p</i>-Convex Functions Involving Recently Defined Quantum Integrals

Gulshan G., Budak H., Hussain R., Ali M. A.

UKRAINIAN MATHEMATICAL JOURNAL, vol.75, pp.1371-1387, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 75
  • Publication Date: 2024
  • Doi Number: 10.1007/s11253-024-02267-1
  • Journal Name: UKRAINIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.1371-1387
  • Kocaeli University Affiliated: No

Abstract

We develop new Hermite-Hadamard-type integral inequalities for p-convex functions in the context of q-calculus by using the concept of recently defined T-q-integrals. Then the obtained Hermite-Hadamard inequality for p-convex functions is used to get a new Hermite-Hadamard inequality for coordinated p-convex functions. Furthermore, we present some examples to demonstrate the validity of our main results. We hope that the proposed ideas and techniques may stimulate further research in this field.