Academic Press Means in Mathematical Analysis: Bivariate Means (Mathematical Analysis and its Applications)

Product Description Means in Mathematical Analysis addresses developments in global analysis, non-linear analysis, and the many problems of associated fields, including dynamical systems, ergodic theory, combinatorics, differential equations, approximation theory, analytic inequalities, functional equations and probability theory. The series comprises highly specialized research monographs written by eminent scientists, handbooks and selected multi-contributor reference works (edited volumes), bringing together an extensive body of information. It deals with the fundamental interplay of nonlinear analysis with other headline domains, particularly geometry and analytic number theory, within the mathematical sciences. Review "This is a very specialized monograph. ...Much of this book is devoted to means. It develops some general properties of means as well as properties of many specific means that are useful with double sequences. It then develops properties of double sequences, especially speed of convergence. This is done both for general sequences and for particular choices of mean." --MAA Reviews Review Comprehensive research monograph that discusses the relationship of means with the classical arithmetic-geometric mean of Gauss From the Back Cover The arithmetic-geometric mean of Gauss is one of the most fascinating themes of mathematical analysis with many open problems related particularly to iteration of means. Means in Mathematical Analysis details many interesting and up-to-date results related to arithmetic-geometric means aimed at motivating and preparing the graduate and first year PhD audience to work on these open problems. This book can also be used as a guide for specific courses within mathematical analysis relating to means. Many results from this work appear for the first time in a book. Reviews double sequences defined with two arbitrary means, aiding digestion, analysis and prospective research in this complex topic for beginning researchers. Provides exact solutions on bounds, inequalities, approximations for researchers interrogating means across physical and statistical problems. Places the current state of means in mathematical analysis alongside its storied and impressive history together with future perspectives and currently unanswered problems, presenting a panorama of knowledge for interested readers. About the Authors Professor Gheorghe Toader (1945-2015) graduated in 1969 from the Faculty of Mathematics at "Babes-Bolyai" University in Cluj-Napoca. In 1980 he defended his PhD thesis. His last position was as a Professor at the Mathematics Department of Technical University of Cluj-Napoca. He has published over 165 scientific papers in the field of Mathematics, of which more than 70 papers related to the subject of this book. Iulia Costin was born in Romania in 1971. She graduated in 1994 from the Faculty of Mathematics and Informatics at "Babes-Bolyai" University in Cluj-Napoca. In 2001 she defended her PhD thesis. Currently she is a Senior Lecturer at the Computer Science Department of Technical University of Cluj-Napoca. She has published more than 30 papers related to the subject of this book. About Mathematics in Science and Engineering Series Editor : Themistocles Rassias Editorial Board : Sever Dragomir, Soon-Mo Jung, Gradimir Milovanovic, Hari Srivastava This new series of highly specialized research monographs, introductory handbooks and selected multi-contributor reference works, addresses developments in global analysis, non-linear analysis and the many problems of associated fields, including dynamical systems, ergodic theory, combinatorics, differential equations, approximation theory, analytic inequalities, functional equations, and probability theory. About the Author Gheorghe Toader was born in Romania in 1945, but deferred research until 1980 when he defended his PhD thesis, and served as Professor at the Depar