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Means in mathematical analysis : bivariate means /
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 probabi...
| Call Number: | Libro Electrónico |
|---|---|
| Main Authors: | , |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
London :
Academic Press,
[2018]
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| Series: | Mathematical analysis and its appllications.
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| Subjects: | |
| Online Access: | Texto completo |
Table of Contents:
- Front Cover; Means in Mathematical Analysis; Copyright; Contents; About the Authors; Preface; Acknowledgment; Introduction; Motivation for this book; Chapter 1; Chapter 2; Chapter 3; Chapter 4; 1 Classical theory of the AGM; 1.1 Measurement of the circle; 1.2 Heron's method of extracting square roots; 1.3 Lagrange and the de nition of the AGM; 1.4 Lemniscatic integrals; 1.5 Elliptic integrals; 1.6 Hypergeometric series; 1.7 Landen's transformation; 1.8 The perimeter of an ellipse; 2 Means; 2.1 Means and properties of means; 2.1.1 Greek means; 2.1.2 De nition and properties of means
- 2.1.3 Quasi-arithmetic means2.1.4 Other methods for the construction of means; 2.1.5 Comparison of means; 2.1.6 Weighted means; 2.1.7 Weak and angular inequalities; 2.1.8 Operations with means; 2.1.9 Universal means; 2.1.10 Invariant means; 2.2 Complementariness; 2.2.1 Complementary means; 2.2.2 Algebraic and topological structures on some set of means; 2.2.3 More about pre-means; 2.2.4 Complementary pre-means; 2.2.5 Partial derivatives of pre-means; 2.2.6 Series expansion of means; 2.2.7 Generalized inverses of means; 2.2.8 Complementariness with respect to power means
- 2.2.9 Complementariness with respect to Lehmer means2.2.10 Complementariness with respect to Gini means; 2.2.11 Complementariness with respect to Stolarsky means; 2.2.12 Complementariness with respect to extended logarithmic means; 2.2.13 Complementariness with respect to the identric mean; 3 Double sequences; 3.1 Archimedean double sequences; 3.2 Determination of A-compound means; 3.3 Rate of convergence of an Archimedean double sequence; 3.4 Acceleration of the convergence; 3.5 Gaussian double sequences; 3.6 Determination of G-compound means
- 3.7 Rate of convergence of a Gaussian double sequence3.8 Comparison of compound means; 3.9 The Schwab-Borchardt mean; 3.10 Seiffert-like means; 3.11 Double sequences with pre-means; 3.12 Other generalizations of double sequences; 4 Integral means; 4.1 The de nition of the integral mean; 4.2 A recurrence formula; 4.3 Gauss' functional equation; 4.4 Special integral means; 4.5 Comparison of integral means; 4.6 Integral pre-means; 4.7 Special pre-means; 4.8 Estimations of some integral means; Bibliography; List of Symbols; Subject Index; Author Index; Back Cover