Right Quantum Calculus on Finite Intervals with Respect to Another Function and Quantum Hermite–Hadamard Inequalities

In this paper, we study right quantum calculus on finite intervals with respect to another function. We present new definitions on the right quantum derivative and right quantum integral of a function with respect to another function and study their basic properties. The new definitions generalize t...

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Bibliographic Details
Published inAxioms Vol. 13; no. 7; p. 466
Main Authors Cuntavepanit, Asawathep, Ntouyas, Sotiris K., Tariboon, Jessada
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2024
Subjects
Calculus
Convex analysis
Derivatives
Inequalities
Inequalities (Mathematics)
Integrals
Intervals
quantum calculus
quantum derivative
quantum integral
Quantum theory
Thailand
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Summary:In this paper, we study right quantum calculus on finite intervals with respect to another function. We present new definitions on the right quantum derivative and right quantum integral of a function with respect to another function and study their basic properties. The new definitions generalize the previous existing results in the literature. We provide applications of the newly defined quantum calculus by obtaining new Hermite–Hadamard-type inequalities for convex, h-convex, and modified h-convex functions.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13070466