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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

5 votes
1 answer
189 views

Conditions under which inequality holds for all triplets of non-negative reals

I have the following inequality: $$ \left(\frac{1}{3} \left( \left(\frac{a+b}{2}\right)^3 + \left(\frac{a+c}{2}\right)^3 + \left(\frac{b+c}{2}\right)^3 \right) \right)^\frac{1} …