An introduction to the theory of functional equations and inequalities: Cauchy's equation and Jensen's inequality

Review of the first edition ‘The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book isby no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszú, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general.’ (Janos Aczel, Mathematical Reviews) INDICE: Introduction.- I. Set Theory.- II. Topology.- III. Measure Theory.- IV. Algebra.- V. Additive Functions and Convex Functions.- VI. Elementary Properties of Convex Functions.- VII. Continuous Convex Functions.- VIII. Inequalities.- IX. Boundedness and Continuity of Convex and Additive Functions.- X. The Classes A, B, C.- XI. Properties of Hamel Bases.- XII. Further Properties of Additive and Convex Functions.- XIII. Related Equations.- XIV. Derivations and Automorphisms.- XV. Convex Functions of Higher Order.- XVI. Subadditive Functions.- XVII. Nearly Additive and Nearly Convex Functions.- XVIII. Extensions of Homomorphisms.- Bibliography.

• ISBN: 978-3-7643-8748-8
• Editorial: Birkhaüser
• Encuadernacion: Rústica
• Páginas: 600
• Fecha Publicación: 01/05/2008
• Nº Volúmenes: 1
• Idioma: Inglés