Generalization of quantum calculus and corresponding Hermite-Hadamard inequalities

Akbar, Saira; Abbas, Mujahid; BUDAK, HÜSEYİN

doi:10.1007/s13324-024-00960-9

Generalization of quantum calculus and corresponding Hermite-Hadamard inequalities

Akbar S. B., Abbas M., BUDAK H.

ANALYSIS AND MATHEMATICAL PHYSICS, cilt.14, sa.5, 2024 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 14 Sayı: 5
Basım Tarihi: 2024
Doi Numarası: 10.1007/s13324-024-00960-9
Dergi Adı: ANALYSIS AND MATHEMATICAL PHYSICS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
Kocaeli Üniversitesi Adresli: Hayır

Özet

The aim of this paper is first to introduce generalizations of quantum integrals and derivatives which are called (phi-h) integrals and (phi-h) derivatives, respectively. Then we investigate some implicit integral inequalities for (phi-h) integrals. Different classes of convex functions are used to prove these inequalities for symmetric functions. Under certain assumptions, Hermite-Hadamard-type inequalities for q-integrals are deduced. The results presented herein are applicable to convex, m-convex, and & hstrok;-convex functions defined on the non-negative part of the real line.