Introduction to functional equations.

*(English)*Zbl 1223.39012
Boca Raton, FL: CRC Press (ISBN 978-1-4398-4111-2/hbk). xviii, 447 p. (2011).

This book outlines the basic mathematical ideas of functional equations and provides the reader with an elementary exposition of the discipline. All functions considered in this book are real or complex valued, which makes the presentation very useful to students of different mathematical disciplines.

In Chapters 1 to 17 the authors present a survey of the classical functional equations (additive Cauchy functional equation, other Cauchy functional equations, Jensen functional equation, Pexider’s functional equations, quadratic functional equation, D’Alembert functional equation, Pompeiu functional equation, Hosszu functional equation, Davison functional equation, Abel functional equation, mean value type functional equations).

Chapters 18 through 24 are devoted to the problem of the Ulam-Hyers stability of some of the functional equations considered in the earlier chapters.

At the end of each chapter there are sets of interesting exercises (many of them are taken from the book of M. Kuczma [An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality. Warszawa-Kraków-Katowice: Państwowe Wydawnictwo Naukowe (1985; Zbl 0555.39004), 2nd ed. Basel: Birkhäuser (2009; Zbl 1221.39041)]). Also included is a bibliography of 339 references and a wide index.

This nice book should be interesting for graduate students and researchers in the field of analysis and functional equations.

In Chapters 1 to 17 the authors present a survey of the classical functional equations (additive Cauchy functional equation, other Cauchy functional equations, Jensen functional equation, Pexider’s functional equations, quadratic functional equation, D’Alembert functional equation, Pompeiu functional equation, Hosszu functional equation, Davison functional equation, Abel functional equation, mean value type functional equations).

Chapters 18 through 24 are devoted to the problem of the Ulam-Hyers stability of some of the functional equations considered in the earlier chapters.

At the end of each chapter there are sets of interesting exercises (many of them are taken from the book of M. Kuczma [An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality. Warszawa-Kraków-Katowice: Państwowe Wydawnictwo Naukowe (1985; Zbl 0555.39004), 2nd ed. Basel: Birkhäuser (2009; Zbl 1221.39041)]). Also included is a bibliography of 339 references and a wide index.

This nice book should be interesting for graduate students and researchers in the field of analysis and functional equations.

Reviewer: Stefan Czerwik (Gliwice)

##### MSC:

39B05 | General theory of functional equations and inequalities |

39B82 | Stability, separation, extension, and related topics for functional equations |

39B22 | Functional equations for real functions |

39B32 | Functional equations for complex functions |

39-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations |