Novelty Hermite-Hadamard-Type Inequalities for Various Convexity Functions and Their Applications
Küçük Resim Yok
Tarih
2025
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Univ Maragheh
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The classical Hermite-Hadamard inequality provides a fundamental estimate for the integral mean of convex functions and has inspired numerous extensions in mathematical analysis. In this paper, we present new generalizations of the Hermite-Hadamard inequality within the framework of fractional calculus by employing the Caputo-Fabrizio fractional integral operator, known for its non-singular kernel and smooth memory effects. Specifically, we establish refined inequalities for convex functions that are three times differentiable and extend these results to the broader class of quasi-convex functions. Furthermore, we demonstrate several applications of the newly derived inequalities to special means, specific functions, the modified Bessel function, quadrature formulas and midpoint formulas. These findings contribute to the expanding body of literature on fractional inequalities and their applications in both theoretical and applied contexts.
Açıklama
Anahtar Kelimeler
Hermite-Hadamard Type Inequality, Quasi-Convex Function, Convex Function, Caputo-Fabrizio Fractional Integrals, Quadrature Formula, Modified Bessel Function, Special Means
Kaynak
Sahand Communications in Mathematical Analysis
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
Cilt
22
Sayı
4
