##
**Functional equations and inequalities in several variables.**
*(English)*
Zbl 1011.39019

Singapore: World Scientific. x, 410 p. (2002).

The author presents his material in three parts: Part I – Functional equations and inequalities in linear spaces – is devoted to familiar functional equations (basic) like Cauchy, D’Alembert, and quadratic equations. This part also contains convex and polynomial functions.

Part II – Ulam-Hyers-Rassias stability of functional equations – is entirely devoted to the examination of the stability problem initially formulated by Ulam with regard to Cauchy functional equation. This section brings out the stability problem of several functional equations like Cauchy, Jensen, Pexider, D’Alembert, gamma, and quadratic, studied by many authors.

Part III – Functional equations in set-valued functions – deals with set-valued functions of Cauchy, Jensen, Pexider, quadratic equations and Hahn-Banach type extensions.

In the preface the author states ‘this book combines the classical theory and examples as well as recent most results in the subject’. Even though the focus is limited in nature, this book contains some new materials and references not found in earlier books on functional equations. Certain references are overemphasized (promoted!) and referred to in places which are not appropriate. At the same time proper references are not cited at appropriate places. However, a book on functional equations is always welcome.

Part II – Ulam-Hyers-Rassias stability of functional equations – is entirely devoted to the examination of the stability problem initially formulated by Ulam with regard to Cauchy functional equation. This section brings out the stability problem of several functional equations like Cauchy, Jensen, Pexider, D’Alembert, gamma, and quadratic, studied by many authors.

Part III – Functional equations in set-valued functions – deals with set-valued functions of Cauchy, Jensen, Pexider, quadratic equations and Hahn-Banach type extensions.

In the preface the author states ‘this book combines the classical theory and examples as well as recent most results in the subject’. Even though the focus is limited in nature, this book contains some new materials and references not found in earlier books on functional equations. Certain references are overemphasized (promoted!) and referred to in places which are not appropriate. At the same time proper references are not cited at appropriate places. However, a book on functional equations is always welcome.

Reviewer: Pl.Kannappan (Waterloo/Ontario)

### MSC:

39Bxx | Functional equations and inequalities |

39-02 | Research exposition (monographs, survey articles) pertaining to difference and functional equations |