{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T13:25:07Z","timestamp":1773753907859,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T00:00:00Z","timestamp":1742515200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, weighted Newton-type inequalities (WN-TI) for multiple classes of functions by employing generalized proportional fractional (GPF) integrals are established. The core step involves establishing a key integral identity under a positive weighting scheme, which underlies all subsequent results. By integrating this identity with GPF operators, we derive various forms of (WN-TI) suitable for several function types, including differentiable convex, bounded, and Lipschitz functions.<\/jats:p>","DOI":"10.3390\/axioms14040234","type":"journal-article","created":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T07:25:00Z","timestamp":1742541900000},"page":"234","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Comprehensive Weighted Newton Inequalities for Broad Function Classes via Generalized Proportional Fractional Operators"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4036-6368","authenticated-orcid":false,"given":"Mohamed A.","family":"Barakat","sequence":"first","affiliation":[{"name":"Department of Basic Science, University College of Al Wajh, University of Tabuk, Tabuk 71491, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Sciences, Al-Azhar University, Assiut 71524, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1186\/s13660-023-02953-x","article-title":"Some new parameterized Newton-type inequalities for differentiable functions via fractional integrals","volume":"2023","author":"Ali","year":"2023","journal-title":"J. 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