New Study on the Quantum Midpoint-Type Inequalities for Twice q-Differentiable Functions via the Jensen-Mercer Inequality
Küçük Resim Yok
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Mdpi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The objective of this study is to identify novel quantum midpoint-type inequalities for twice q-differentiable functions by utilizing Mercer's approach. We introduce a new auxiliary variant of the quantum Mercer midpoint-type identity related to twice q-differentiable functions. By applying the theory of convex functions to this identity, we introduce new bounds using well-known inequalities, such as Holder's inequality and power-mean inequality. We provide explicit examples along with graphical demonstrations. The findings of this study explain previous studies on midpoint-type inequalities. Analytic inequalities of this type, as well as related strategies, have applications in various fields where symmetry plays an important role.
Açıklama
Anahtar Kelimeler
quantum calculus, convex functions, midpoint inequalities, Jensen-Mercer inequality, Refinements, Convex
Kaynak
Symmetry-Basel
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
Cilt
15
Sayı
5
