Some new (p,q)$$ \left(p,q\right) $$‐Hadamard‐type integral inequalities for the generalized m$$ m $$‐preinvex functions

Abstract

This paper introduces and establishes new Hermite‐Hadamard type inequalities specifically tailored for ‐preinvex functions within the ‐calculus framework. These newly developed inequalities come with accompanying left‐right estimates, which enhance their practical utility. The primary objective of this research is to investigate the properties of ‐differentiable ‐preinvex functions and derive inequalities that extend and generalize existing results in the domain of integral inequalities. The techniques employed in this study hold broader implications, finding relevance in various fields where symmetry is paramount. The findings presented in this paper make a significant contribution to the field of analytic inequalities, offering valuable insights into the behavior and characteristics of ‐preinvex functions. Moreover, the established results demonstrate the wider applicability and generalization of analogous findings from prior literature. The techniques and inequalities introduced herein pave the way for further exploration and research in the realm of integral inequalities.