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- Title
New Study on the Quantum Midpoint-Type Inequalities for Twice q -Differentiable Functions via the Jensen–Mercer Inequality.
- Authors
Butt, Saad Ihsan; Umar, Muhammad; Budak, Hüseyin
- 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 H"older'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.
- Subjects
MERCER LLC; CONVEX functions; IDENTITIES (Mathematics); SYMMETRY
- Publication
Symmetry (20738994), 2023, Vol 15, Issue 5, p1038
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym15051038