J. Nonl. Mod. Anal., 7 (2025), pp. 135-177.
Published online: 2025-02
[An open-access article; the PDF is free to any online user.]
Cited by
- BibTex
- RIS
- TXT
This article mainly studies some new discrete Hermite-Hadamard inequalities for integer order and fractional order. For this purpose, the definitions of $h$-convexity and preinvexity for a real-valued function $f$ defined on a set of integers $\mathbb{Z}$ are introduced. Under these two new definitions, some new discrete Hermite-Hadamard inequalities for integer order related to the endpoints and the midpoint $\frac{a+b}{2}$ based on the substitution rules are proposed, and they are generalized to fractional order forms. In addition, for the $h$-convex function on the time scale $\mathbb{Z},$ two new discrete Hermite-Hadamard inequalities for integer order by dividing the time scale differently are obtained.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.135}, url = {http://global-sci.org/intro/article_detail/jnma/23837.html} }This article mainly studies some new discrete Hermite-Hadamard inequalities for integer order and fractional order. For this purpose, the definitions of $h$-convexity and preinvexity for a real-valued function $f$ defined on a set of integers $\mathbb{Z}$ are introduced. Under these two new definitions, some new discrete Hermite-Hadamard inequalities for integer order related to the endpoints and the midpoint $\frac{a+b}{2}$ based on the substitution rules are proposed, and they are generalized to fractional order forms. In addition, for the $h$-convex function on the time scale $\mathbb{Z},$ two new discrete Hermite-Hadamard inequalities for integer order by dividing the time scale differently are obtained.