Deriving weighted Newton-type inequalities for diverse function classes through Riemann–Liouville fractional integrals

Areej A. Almoneef, Abd-Allah Hyder and Hüseyin Budak

Chaos, Solitons & Fractals, 2024, vol. 186, issue C

Abstract: This study introduces weighted Newton-type inequalities for diverse function classes via Riemann–Liouville fractional integrals. We begin by employing a positive weighted function to demonstrate a crucial integral equality which necessary for establishing the main outcomes. Leveraging this equality along with Riemann–Liouville fractional integrals, we prove several weighted Newton-type inequalities for various function classes, including differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. From the obtained results, one can get an insights into the implications of Newton-type inequalities and outlines potential avenues for future research endeavors.

Keywords: Weighted inequalities; Newton-type inequalities; Fractional integral inequalities (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924007574

DOI: 10.1016/j.chaos.2024.115205

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