TY - JOUR
T1 - A Novel Variant of Milne’s Rule Inequalities on Quantum Calculus for Convex Functions with Their Computational Analysis
AU - Haider , Wali
AU - Budak , Hüseyin
AU - Shehzadi , Asia
AU - Hezenci , Fatih
AU - Chen , Haibo
JO - Journal of Nonlinear Modeling and Analysis
VL - 5
SP - 1727
EP - 1745
PY - 2025
DA - 2025/09
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1727
UR - https://global-sci.org/intro/article_detail/jnma/24386.html
KW - Milne’s inequality, $q$-calculus, convex functions.
AB - <p style="text-align: justify;">In this investigation, we introduce a novel approach for establishing Milne’s type inequalities in the context of quantum calculus for differentiable convex functions. First, we prove a quantum integral identity. We
derive numerous new Milne’s rule inequalities for quantum differentiable convex functions. These inequalities are relevant in open Newton-Cotes formulas,
as they facilitate the determination of bounds for Milne’s rule applicable to
differentiable convex functions in both classical and $q$-calculus. In addition,
we conduct a computational analysis of these inequalities for convex functions
and provide mathematical examples to demonstrate the validity of the newly
established results within the framework of $q$-calculus.</p>