Asymptotic expansions of stable, stabilizable and stabilized means with applications

In this paper we present a complete asymptotic expansion of a symmetric homogeneous stable (balanced), stabilizable and stabilized mean. By including known asymptotic expansions of parametric means it is shown how the obtained coefficients are used to solve the problem of identifying stable means within classes of parametric means under consideration, how to disprove some mean is stabilizable or stabilized and how to obtain best possible parameters such that given mean is sub-stabilizable with a pair of parametric means.