Fractional Integral Estimates of Boole Type: Majorization and Convex Function Approach with Applications
Key Points
The aim is to enhance estimates for differentiable functions using a Boole-type inequality framework.
Incorporated fractional integral operators into a new auxiliary identity
Applied majorization theory in combination with classical inequalities
Examined special functions and quadrature rules in real-world examples
Established sharp bounds utilizing the properties of convex functions
Extended existing results in mathematical literature through new methodologies
Combined various classical inequalities such as Power mean and Hölder inequalities
Abstract
The goal of this paper is to use a Boole-type inequality framework to provide better estimates for differentiable functions. Using majorization theory, fractional integral operators are incorporated into a new auxiliary identity. The method establishes sharp bounds by combining the properties of convex functions with classical inequalities like the Power mean and Hölder inequalities, as well as the Niezgoda–Jensen–Mercer (NJM) inequality for majorized tuples. Additionally, the study presents real-world examples involving special functions and examines pertinent quadrature rules. This work’s primary contribution is the extension and generalization of a number of results that are already known in the current body of mathematical literature.