DSpace Arşivi :: by Yazar "Umar, Muhammad" değerine göre listeleniyor

Listeleniyor 1 - 2 / 2

New Study on the Quantum Midpoint-Type Inequalities for Twice q-Differentiable Functions via the Jensen-Mercer Inequality
(Mdpi, 2023) Butt, Saad Ihsan; Umar, Muhammad; Budak, Hüseyin
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.
Novel q-Differentiable Inequalities
(Mdpi, 2023) Zuo, Xuewu; Butt, Saad Ihsan; Umar, Muhammad; Budak, Hüseyin; Ali, Muhammad Aamir; Dolgy, Dmitry V.
The striking goal of this study is to introduce a q-identity for a parameterized integral operator via differentiable function. First, we discover the parameterized lemma for the q-integral. After that, we provide several q-differentiable inequalities. By taking suitable choices, some interesting results are obtained. With all of these, we displayed the findings from the traditional analysis utilizing q & RARR;1-.