Refined Ostrowski-Type Inequalities via Multistep Quadratic Kernel with Applications to CDFs and Data Science

Refined Ostrowski-Type Inequalities via Multistep Quadratic Kernel

Abstract

The study presents a refined framework of Ostrowski-type inequalities by using a multistep quadratic kernel for functions whose first derivatives are of bounded variation. This novel approach not only generalizes classical results but also establishes tighter bounds applicable to cumulative distribution function and data science scenarios. Furthermore, we demonstrate the relevance of the results by applying through analysis of the logistic and hyperbolic tangent functions, which are commonly used in classification tasks and neural network. The developed inequalities enhance the precision of error estimates in data-driven computations, validating their usefulness in real-world applications.