MathDB

Inequality on k variables

Source:

October 7, 2010

inequalitiesinequalities proposed

Problem Statement

Given positive integers

k,m, n

with

km \leq n

and non-negative real numbers

x_1, \ldots , x_k

, prove that

n \left( \prod_{i=1}^k x_i^m -1 \right) \leq m \sum_{i=1}^k (x_i^n-1).