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find the minimum value

Source: Poland 1975

August 28, 2013
limitinequalities unsolvedinequalities

Problem Statement

consider 0<u<10<u<1. find α>0\alpha > 0 minimum such that there exists β>0\beta > 0 satisfying (1+x)u+(1−x)u≤2−xαβ∀0<x<1(1+x)^u +(1-x)^u \leq 2 - \frac{x^\alpha}{\beta} \forall 0<x<1
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