@Article{JNMA-7-1,
author = {Xiaoyue, Han and Xu, Run},
title = {Some New Discrete Hermite-Hadamard Inequalities and Their Generalizations},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2025},
volume = {7},
number = {1},
pages = {135--177},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2025.135},
url = {https://global-sci.com/article/91685/some-new-discrete-hermite-hadamard-inequalities-and-their-generalizations}
}