Benaissa, BouharketAzzouz, NoureddineSarikaya, Mehmet Zeki2025-10-112025-10-1120241687-2770https://doi.org/10.1186/s13661-024-01952-1https://hdl.handle.net/20.500.12684/21730This study establishes Newton-type inequalities for third differentiable and s-convex functions that use the Riemann integral. New Newton-type inequalities are also introduced using a summation parameter p >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p\geq 1$\end{document} for various convexity cases.en10.1186/s13661-024-01952-1info:eu-repo/semantics/openAccesss-convex functionNewton inequalityH & ouml;lder inequalityRiemann integralArticle202412-s2.0-85207804541WOS:001344807400001Q1Q1