Abstract
The exponential function \(f(x)=e^x\) is a powerful tool in each field of natural sciences and engineering since many natural phenomena well-known to us can be described best of all by means of it. The famous exponential functional equation \(f(x+y)=f(x)f(y)\) simplifies the elegant property of the exponential function, for example, exCy D exey. In Section 9.1, the superstability of the exponential functional equation will be proved. Section 9.2 deals with the stability of the exponential equation in the sense of R. Ger. Stability problems of the exponential functional equation on a restricted domain and asymptotic behaviors of exponential functions are discussed in Section 9.3. Another exponential functional equation \(f(xy)=f(x)^y\) will be introduced in Section 9.4.
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© 2011 Springer Science+Business Media, LLC
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Jung, SM. (2011). Exponential Functional Equations. In: Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis. Springer Optimization and Its Applications(), vol 48. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9637-4_9
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DOI: https://doi.org/10.1007/978-1-4419-9637-4_9
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