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Newton-Type Inequalities in the Context of Generalized Fractional Integrals via Several Function Classes

Author

Listed:
  • Ä°rem Çay
  • Hüseyin Budak
  • Ä°rem BaÄŸlan
  • Ercan Çelik

Abstract

In this paper, we investigate some new Newton-type inequalities involving generalized fractional integrals by using different function classes. For this aim, we first prove an identity for differentiable functions. Then, by this equality, we prove several Newton-type inequalities for the function classes such as convex functions, bounded functions, Lipschitzian functions, and functions of bounded variations. We also show that the main results generalize some existing results for classical integrals and Riemann–Liouville fractional integrals.

Suggested Citation

  • Ä°rem Çay & Hüseyin Budak & Ä°rem BaÄŸlan & Ercan Çelik, 2026. "Newton-Type Inequalities in the Context of Generalized Fractional Integrals via Several Function Classes," Journal of Mathematics, Hindawi, vol. 2026, pages 1-13, July.
    • Handle: RePEc:hin:jjmath:4909600
    DOI: 10.1155/jom/4909600
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