Functional Equations - Results and Advances

The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century. First of all, this is due to the fact that the mathematical applications raised the investigations of newer and newer types of functional equations. At the same time, the self development of this theory was also very fruitful. This can be followed in many monographs that treat and discuss the various methods and approaches. These developments were also essentially influenced by a number jour nals, for instance, by the Publicationes Mathematicae Debrecen (founded in 1953) and by the Aequationes Mathematicae (founded in 1968), be cause these journals published papers from the field of functional equa tions readily and frequently. The latter journal also publishes the yearly report of the International Symposia on Functional Equations and a comprehensive bibliography of the most recent papers. At the same time, there are periodically and traditionally organized conferences in Poland and in Hungary devoted to functional equations and inequali ties. In 2000, the 38th International Symposium on Functional Equations was organized by the Institute of Mathematics and Informatics of the University of Debrecen in Noszvaj, Hungary. The report about this meeting can be found in Aequationes Math. 61 (2001), 281-320.

List of contents

I. Classical Functional Equations and Inequalities.- On some trigonometric functional inequalities.- On the continuity of additive-like functions and Jensen convex functions which are Borel on a sphere.- Note on a functional-differential inequality.- A characterization of stationary sets for the class of Jensen convex functions.- On the characterization of Weierstrass's sigma function.- On a Mikusi?ski-Jensen functional equation.- II. Stability of Functional Equations.- Stability of the multiplicative Cauchy equation in ordered fields.- On approximately monomial functions.- Les opérateurs de Hyers.- Geometrical aspects of stability.- III. Functional Equations in One Variable and Iteration Theory.- On semi-conjugacy equation for homeomorphisms of the circle.- A survey of results and open problems on the Schilling equation.- Properties of an operator acting on the space of bounded real functions and certain subspaces.- IV. Composite Functional Equations and Theory of Means.- A Matkowski-Sutô type problem for quasi-arithmetic means of order ?.- An extension theorem for conjugate arithmetic means.- Homogeneous Cauchy mean values.- On invariant generalized Beckenbach-Gini means.- Final part of the answer to a Hilbert's question.- V. Functional Equations on Algebraic Structures.- A generalization of d'Alembert's functional equation.- About a remarkable functional equation on some restricted domains.- On discrete spectral synthesis.- Hyers theorem and the cocycle property.- VI. Functional Equations in Functional Analysis.- Mappings whose derivatives are isometries.- Localizable functionals.- Jordan maps on standard operator algebras.- VII. Bisymmetry and Associativity Type Equations on Quasigroups.- On the functional equation S1(x, y) = S2(x, T(N(x), y)).-Generalized associativity on rectangular quasigroups.- The aggregation equation: solutions with non intersecting partial functions.

Summary

The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century. First of all, this is due to the fact that the mathematical applications raised the investigations of newer and newer types of functional equations. At the same time, the self development of this theory was also very fruitful. This can be followed in many monographs that treat and discuss the various methods and approaches. These developments were also essentially influenced by a number jour­ nals, for instance, by the Publicationes Mathematicae Debrecen (founded in 1953) and by the Aequationes Mathematicae (founded in 1968), be­ cause these journals published papers from the field of functional equa­ tions readily and frequently. The latter journal also publishes the yearly report of the International Symposia on Functional Equations and a comprehensive bibliography of the most recent papers. At the same time, there are periodically and traditionally organized conferences in Poland and in Hungary devoted to functional equations and inequali­ ties. In 2000, the 38th International Symposium on Functional Equations was organized by the Institute of Mathematics and Informatics of the University of Debrecen in Noszvaj, Hungary. The report about this meeting can be found in Aequationes Math. 61 (2001), 281-320.

Product details

• Assisted by: Zolta Daroczy (Editor), Zoltan Daroczy (Editor), Zoltán Daróczy (Editor), Páles (Editor), Páles (Editor), Zsolt Páles (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 21.10.2010
• EAN: 9781441952103
• ISBN: 978-1-4419-5210-3
• No. of pages: 361
• Illustrations: X, 361 p.
• Series: Advances in Mathematics; Advances in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis