Refined Ostrowski-type inequalities via multistep quadratic kernel with applications to CDFs and data science

Muhammad Muawwaz; Muhammad Maaz; Ather Qayyum; Ibrahim K.  Alsulami; Mahnoor Fatima; Muhammad Yasir Arif

doi:10.5269/bspm.78108

Muhammad Muawwaz Department of Mathematics, University of Southern Punjab Multan, Pakistan.
Muhammad Maaz Department of Mathematics, University of Southern Punjab, Multan, Pakistan.
Ather Qayyum Department of Mathematics, University of Southern Punjab Multan, Pakistan.
Ibrahim K. Alsulami Department of Science, King Abdulaziz Military Academy (KAMA), Riyadh 13959, Saudi Arabia
Mahnoor Fatima Department of Mathematics, University of Southern Punjab Multan, Pakistan.
Muhammad Yasir Arif Department of Mathematics, University of Southern Punjab Multan, Pakistan.

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.

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