Let $X$ be a Banach space. Then is complemented in the bidual $X^{**}$ if and only there exists an invariant mean $\ell _\infty (G, X)\to X$ with respect to free Abelian group $G$ of rank equal cardinality $X^{**}$, this happens

In this paper, we introduce the notion of invariant pseudolinearity for nondifferentiable and nonconvex functions by means of Dini directional derivatives. We present some characterizations of invariant pseudolinear functions. Some characterizations of the solution set of a nonconvex and nondifferentiable, but invariant, pseudolinear program are obtained. The results of this paper extend variou...

We prove dimension-invariant imbedding theorems for Sobolev spaces using extrapolation means.

We study invariance in the class of weighted Lehmer means. Thus we look at triples of weighted Lehmer means with the property that one is invariant with respect to the other two.