Stability of a system of generalized trigonometric equations
Abstract
Addition formulas for generalized trigonometric functions corresponding to a given symmetric bounded and convex planar set containing the origin as an inner point are derived. Connections with the theory of characters on (semi) groups are considered. Hyers-Ulam stability of a suitable system of functional equations is investigated. It is also shown that superstability phenomenon fails to hold for that system.
References
2. R. Ger, P. Šemrl, On the stability of the exponential functions, Proc. Amer. Math. Soc. (to appear).
Instytut Matematyki, Wyższa Szkoła Pedagogiczna w Częstochowie Poland
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