On Improved Simpson-Type Inequalities via Convexity and Generalized Fractional Operators
Küçük Resim Yok
Tarih
2025
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Wiley
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this work, we develop novel Simpson-type inequalities for mappings with convex properties by employing operators for tempered fractional integrals. These findings expand upon and refine classical results, including those linked to Riemann-Liouville fractional integrals. Using methodologies such as H & ouml;lder's inequality, the power-mean inequality, and convex function properties, we derive precise bounds for these inequalities. The main contributions include the derivation of Simpson-type inequalities under various convexity conditions and their adaptations for specific cases, such as functions with bounded derivatives and Lipschitz continuity. Special cases, where these inequalities reduce to classical results involving standard integrals, are also explored. Explicitly, clear connections to classical integral inequalities are established for differentiable functions whose derivatives satisfy convexity, boundedness, and Lipschitz conditions. Additionally, future research directions are proposed, emphasizing the broad applicability of these results in fractional calculus and convex analysis.
Açıklama
Anahtar Kelimeler
convex function analysis, integral inequality applications, Simpson-type inequalities, tempered fractional calculus
Kaynak
Journal of Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Cilt
2025
Sayı
1
