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

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

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.

Suggested Citation

  • Almoneef, Areej A. & Hyder, Abd-Allah & Budak, Hüseyin, 2024. "Deriving weighted Newton-type inequalities for diverse function classes through Riemann–Liouville fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924007574
    DOI: 10.1016/j.chaos.2024.115205
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    References listed on IDEAS

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    1. Waewta Luangboon & Kamsing Nonlaopon & Jessada Tariboon & Sotiris K. Ntouyas, 2021. "Simpson- and Newton-Type Inequalities for Convex Functions via ( p , q )-Calculus," Mathematics, MDPI, vol. 9(12), pages 1-21, June.
    2. Badreddine Meftah & Hamid Boulares & Ramsha Shafqat & A. Ben Makhlouf & Ramzi Benaicha & Thanin Sitthiwirattham, 2023. "Some New Fractional Weighted Simpson Type Inequalities for Functions Whose First Derivatives Are Convex," Mathematical Problems in Engineering, Hindawi, vol. 2023, pages 1-19, September.
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