Parameterized Newton-type inequalities associated with convex functions via quantum calculus

Year 2025, Volume: 74 Issue: 2, 238 - 253, 19.06.2025

Muhammad Umar , Saad Ihsan Butt Dr. , Hüseyin Budak

https://doi.org/10.31801/cfsuasmas.1434544

Abstract

Using the concept of quantum derivatives and integrals, we first develop a new parameterized identity in this work. This parameterized quantum identity is used to demonstrate parameterized quantum Newton-type inequalities related to convex functions. We also demonstrate how setting $\mathit{q} \to 1^{-}$ allows the newly generated inequalities to be recovered into some existing inequalities. In order to validate the recently discovered inequalities, we conclude by providing mathematical examples of convex functions along with some graphical analysis.

Keywords

Newton-type inequality , convex functions , quantum calculus

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