# Hermite-Hadamard integral inequality

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

$$f(\frac{a+b}{2})\le \frac{1}{b-a}{\int}_{a}^{b}f(t)\mathit{d}t\le \frac{f(a)+f(b)}{2}.$$ |

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 |