Weighted Simpson-Type Quantum Integral Inequalities for h-Convex Functions
MATHEMATICS, vol.14, no.13, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 14 Issue: 13
- Publication Date: 2026
- Doi Number: 10.3390/math14132436
- Journal Name: MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Karadeniz Technical University Affiliated: Yes
Abstract
This paper establishes a weighted Simpson-type identity on the parameter domain associated with quantum integral operators. Using this identity together with H & ouml;lder's inequality and the power mean inequality, we derive new estimates for classes of functions whose associated parameter-domain q-derivatives satisfy h-convexity assumptions. Additional bounds are obtained under boundedness and Lipschitz conditions. Applications to the s-moment of a random variable and to several special means are derived in the classical limit q -> 1- .