Hermite-Hadamard integral inequality

Let $f:[a,b]\to ℝ$ be a convex function. Then

$$f(\frac{a+b}{2})\le \frac{1}{b-a}{\int }_a^{b}f(t)𝑑t\le \frac{f(a)+f(b)}{2}.$$

Title	Hermite-Hadamard integral inequality
Canonical name	HermiteHadamardIntegralInequality
Date of creation	2013-03-22 16:56:30
Last modified on	2013-03-22 16:56:30
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	8
Author	Mathprof (13753)
Entry type	Theorem
Classification	msc 26D15
Classification	msc 26D10