SOME NEW INTEGRAL INEQUALITIES VIA GENERALIZED WEIGHTED OPERATORS AND THEIR CONSEQUENCES НЕКОТОРЫЕ НОВЫЕ ИНТЕГРАЛЬНЫЕ НЕРАВЕНСТВА С ИСПОЛЬЗОВАНИЕМ ОБОБЩЁННЫХ ВЕСОВЫХ ОПЕРАТОРОВ И ИХ СЛЕДСТВИЯ
Chelyabinsk Physical and Mathematical Journal, vol.11, no.2, pp.288-301, 2026 (Scopus)
- Publication Type: Article / Article
- Volume: 11 Issue: 2
- Publication Date: 2026
- Doi Number: 10.47475/2500-0101-2026-11-2-288-301
- Journal Name: Chelyabinsk Physical and Mathematical Journal
- Journal Indexes: Scopus
- Page Numbers: pp.288-301
- Keywords: Hermite–Hadamard inequality, Hölder inequality, modified (h,m)-convexity, power mean inequality, Riemann–Liouville fractional integral, weighted integral, Young inequality
- Bursa Uludag University Affiliated: Yes
Abstract
Fractional integral operators constitute one of the most advanced and effective analytical frameworks for developing new integral inequalities, primarily due to their ability to generalize a wide range of well–known results. In this study, we establish new integral inequalities within the framework of weighted integrals, which extend and generalize Hermite–Hadamard-type inequalities for differentiable functions with modified (h,m)-convexity of the second type. From the main results, we derive several corollaries, particularly for the Riemann and Riemann–Liouville fractional integrals.