Abstract
There are a number of variations of the additive Cauchy functional equation, for example, generalized additive Cauchy equations appearing in Chapter 3, Hosszú’s equation, homogeneous equation, linear functional equation, etc. However, Jensen’s functional equation is the simplest and the most important one among them. The Hyers–Ulam–Rassias stability problems of Jensen’s equation are proved in Section 7.1, and the Hyers–Ulam stability problems of that equation on restricted domains will be discussed in Section 7.2. Moreover, the stability result on a restricted domain will be applied to the study of an asymptotic property of additive functions. In Section 7.3, another approach to prove the stability will be introduced. This approach is called the fixed point method. The superstability and Ger type stability of the Loba?cevski?i functional equation will be surveyed in the last section.
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