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Super-stability and stability of the exponential equations. (English) Zbl 1192.39026

Authors’ abstract: We introduce the concepts of super-stability, stability, \(\delta\)-Ger-stability of the exponential equation of an operator from a normed space into a normed algebra. By using some results due to J. A. Baker [Proc. Am. Math. Soc. 80, 411–416 (1980; Zbl 0448.39003)] and R. Ger and P. Semrl [Proc. Am. Math. Soc. 124, No. 3, 779–787 (1996; Zbl 0846.39013)], we obtain some new conclusions about these stabilities.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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