New Study on the Quantum Midpoint-Type Inequalities for Twice q-Differentiable Functions via the Jensen-Mercer Inequality
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
Mdpi
Access Rights
info:eu-repo/semantics/openAccess
Abstract
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.
Description
Keywords
quantum calculus, convex functions, midpoint inequalities, Jensen-Mercer inequality, Refinements, Convex
Journal or Series
Symmetry-Basel
WoS Q Value
Q2
Scopus Q Value
Q2
Volume
15
Issue
5
