Abstract
For positive scalars a and b the contraharmonic mean of a and b, $C(a,b)$, is defined by \[ C(a,b) = (a^2 + b^2 )/(a + b). \] In this paper we consider a natural matrix generalization of the contraharmonic mean, fit this into the matrix analogue of some of the classical scalar inequalities for means, develop computational procedures which let us generate the matrix analogues of an infinite family of scalar means, and study fixed point problems. Finally, we mention a relationship between least squares problems and the contraharmonic mean.
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