| Description |
1 online resource (xx, 204 pages) |
| Series |
Mathematical analysis and its appllications |
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Mathematical analysis and its appllications
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| 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 |
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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 |
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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 |
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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 |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 181-193) and index |
| Notes |
Vendor-supplied metadata |
| Subject |
Analysis of means.
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Mathematical analysis.
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MATHEMATICS -- Applied.
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MATHEMATICS -- Probability & Statistics -- General.
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Analysis of means
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Mathematical analysis
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| Form |
Electronic book
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| Author |
Costin, Iulia, author.
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| ISBN |
9780128110812 |
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0128110813 |
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0128110805 |
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9780128110805 |
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