Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter, the stability problem is treated in general. In particular, stability of the multiplicative function, logarithmic function, trigonometric functions, vector-valued functions, alternative Cauchy equation, polynomial equation, and quadratic equation is treated. S.M. Ulam, in his famous lecture in 1940 to the Mathematics Club of the University of Wisconsin, presented a number of unsolved problems. This is the starting point of the theory of the stability of functional equations. One of the questions led to a new line of investigation, nowadays known as the stability problems.


Banach Space Functional Equation Commutative Semigroup Riesz Space Normed Algebra 
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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada

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