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The stability of Homomorphisms and Amenability, with applications to functional equations.

The stability of Homomorphisms and Amenability, with applications to functional equations. Abh. Math. Sem. Univ. Hamburg 57, 215-226 (1987) The stability of Homomorphisms and Amenability, with applications to functional equations. by G. L. FORTI 1. Introduction. The investigation in respect of the stability of homomorphisms, i. e. of the Cauchy functional equation, was proposed in 1940 by S. M. ULAM during a talk before the Mathematics Club of the University of Wisconsin. D. H. HYERS solved the problem in 1941 (see [8] and Theorem 1 of the present paper). In the last ten years this result has been used by many authors, especially by people working in the field of functional equations. This led to a great number of papers dealing with generalizations of HYERS' result in different directions (see, for instance, the vast bibliography in [9]). Others important investigations have used the stability of homomorphisms in order to solve some non-homogeneous functional equations and in particular alternative functional equations of Cauchy type. As far as I know the first result of this kind is in [3]. The original HVERS' theorem holds when the mapping involved is defined on an abelian group. This yields to the following question: is this fact indeed essential? The answer is no. L. SZ~rd~LYnlDI in http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

The stability of Homomorphisms and Amenability, with applications to functional equations.

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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Mathematics, general; Algebra; Differential Geometry; Number Theory; Topology; Geometry
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/BF02941612
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Abstract

Abh. Math. Sem. Univ. Hamburg 57, 215-226 (1987) The stability of Homomorphisms and Amenability, with applications to functional equations. by G. L. FORTI 1. Introduction. The investigation in respect of the stability of homomorphisms, i. e. of the Cauchy functional equation, was proposed in 1940 by S. M. ULAM during a talk before the Mathematics Club of the University of Wisconsin. D. H. HYERS solved the problem in 1941 (see [8] and Theorem 1 of the present paper). In the last ten years this result has been used by many authors, especially by people working in the field of functional equations. This led to a great number of papers dealing with generalizations of HYERS' result in different directions (see, for instance, the vast bibliography in [9]). Others important investigations have used the stability of homomorphisms in order to solve some non-homogeneous functional equations and in particular alternative functional equations of Cauchy type. As far as I know the first result of this kind is in [3]. The original HVERS' theorem holds when the mapping involved is defined on an abelian group. This yields to the following question: is this fact indeed essential? The answer is no. L. SZ~rd~LYnlDI in

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals

Published: Dec 1, 1987

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