DOI: 10.3390/axioms13020114 ISSN: 2075-1680
Hermite–Hadamard–Mercer Inequalities Associated with Twice-Differentiable Functions with Applications
Muhammad Aamir Ali, Thanin Sitthiwirattham, Elisabeth Köbis, Asma Hanif- Geometry and Topology
- Logic
- Mathematical Physics
- Algebra and Number Theory
- Analysis
In this work, we initially derive an integral identity that incorporates a twice-differentiable function. After establishing the recently created identity, we proceed to demonstrate some new Hermite–Hadamard–Mercer-type inequalities for twice-differentiable convex functions. Additionally, it demonstrates that the recently introduced inequalities have extended certain pre-existing inequalities found in the literature. Finally, we provide applications to the newly established inequalities to verify their usefulness.