PROOF PERTAINING TO SOME IMPORTANT PROPERTIES OF q-INTEGRAL

Alp N., Sarikaya M. Z., Kunt E., Udak H.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.55, no.6, pp.1499-1511, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 6
  • Publication Date: 2025
  • Doi Number: 10.1216/rmj.2025.55.1499
  • Journal Name: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.1499-1511
  • Karadeniz Technical University Affiliated: Yes

Abstract

In most studies on quantum integral inequalities, the properties of the Riemann integral were also provided for the quantum integral. Due to the misuse of these properties, many studies include some mistakes. In this paper, counterexamples are given first; the properties that cause mistakes are not provided. Moreover, the correct versions of these properties are proved under some conditions. We believe that this study will be an important reference for authors who study quantum integral inequalities.