Means in mathematical analysis. Bivariate means (Q524754)

The book under review, written by the late Professor Gh. Toader, and his daughter I. Costin, contains subjects on means (mainly variate means) and double sequences connected with means. One of the main topics of the book is the arithmetic-geometric mean of Gauss, which is one of the most fascinating themes of mathematics, with many solved and unsolved problems (related particularly to iteration of means). This mean is strongly connected to such important subjects as lemniscate or elliptic integrals, hypergeometric series and their applications, etc. The authors also investigate a general theory of double sequences connected with means, as the Archimedian double sequences, Gaussian double sequences, the Schwab-Borchardt mean, along with the particular famous means, as the Seiffert and Neuman-Sándor means. A special chapter of the book is on complementary means and pre-means, studying algebraic and topological structures on some sets of means; as well as series representations of means. Another chapter deals with integral means and specially the comparison results, as well as estimates for these important means. This well written and nice book is an ideal source for undergraduate or graduate and PhD audience students, or for special courses within mathematical analysis. It could be also a reference work for researchers and scientists working in the extensive field of means and their inequalities or in their various applications in mathematics or physical sciences.