Given two positive numbers , the Gaussian iteration
converges to the Schwab-Borchardt mean of which can be expressed explicitely as
if . This mean is homogeneous but nonsymmetric. Due to various representations of this mean, if and are replaced by the arithmetic, geometric and quadratic means of and one obtains various classical two variable means, e.g., results the logarithmic mean. The so-called Seiffert means can also be obtained this way.
The main results of the paper offer comparison and Ky Fan type inequalities for the Schwab-Borchardt mean, logarithmic mean, the Seiffert-type means, and the Gauss arithmetic-geometric mean. The sequential method of Sándor is generalized to obtain bounds for the means under discussion.