On the superstability of the cosine and sine type functional equations

Lehlou, Fouad; Moussa, Mohammed; Roukbi, Ahmed; Kabbaj, Samir

doi:10.1515/aupcsm-2016-0010

Abstract

In this paper, we study the superstablity problem of the cosine and sine type functional equations: $f (x σ (y) a) + f (xya) = 2 f (x) f (y)$ $$f(x\sigma (y)a) + f(xya) = 2f(x)f(y)$$ and $f (x σ (y) a) - f (xya) = 2 f (x) f (y),$ $$f(x\sigma (y)a) - f(xya) = 2f(x)f(y),$$ where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.

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On the superstability of the cosine and sine type functional equations

Abstract

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