MathDB
Miklos Schweitzer 1969_4

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October 15, 2008
inequalitieslogarithmsreal analysisreal analysis unsolved

Problem Statement

Show that the following inequality hold for all k≥1 k \geq 1, real numbers a1,a2,...,ak a_1,a_2,...,a_k, and positive numbers x1,x2,...,xk. x_1,x_2,...,x_k. \ln \frac {\sum\limits_{i \equal{} 1}^kx_i}{\sum\limits_{i \equal{} 1}^kx_i^{1 \minus{} a_i}} \leq \frac {\sum\limits_{i \equal{} 1}^ka_ix_i \ln x_i}{\sum\limits_{i \equal{} 1}^kx_i} . L. Losonczi
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