Some New Weighted Boole’s type Inequalities for Differentiable Generalize Convex Functions with Their Applications

Abstract

This paper presents a rigorous proof of integral inequalities for first time differentiable h-convex functions. The use of h-convex function extends the results for convex functions and cover a large class of functions, which is the main motivation of using h-convexity. Initially, we derive a weighted Boole’s formula integral identity tailored for differentiable functions. Leveraging this
novel identity, we subsequently establish weighted Boole’s formula type inequalities specifically tailored for differentiable generalize convex functions. We meticulously examine numerous special cases to provide comprehensive insights. These newly derived inequalities offer valuable tools for determining error bounds in various numerical integration techniques within classical calculus. To underscore the efficacy of our principal findings, we offer practical applications to weighted Boole’s type quadrature formulas, continuous random variables, and special means for real numbers. These approximations highlighting their potential impact on computational mathematics and
related fields. Furthermore, we provide numerical examples of newly established inequalities to demonstrate that the results presented in this paper are numerically valid.