Abstract
Let G be a group, \({\mathbb{C}}\) be the field of complex numbers, z 0 be any fixed, nonzero element in the center Z(G) of the group G, and \({\sigma : G \to G}\) be an involution. The main goals of this paper are to study the functional equations \({f(x{\sigma}yz_{0}) - f(xyz_{0}) = 2f(x)f(y)}\) and \({f(x{\sigma}yz_{0}) + f(xyz_{0}) = 2f(x)f(y)}\) for all \({x, y \in G}\) and some fixed element z 0 in the center Z(G) of the group G.
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Perkins, A.M., Sahoo, P.K. On two functional equations with involution on groups related to sine and cosine functions. Aequat. Math. 89, 1251–1263 (2015). https://doi.org/10.1007/s00010-014-0309-z
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DOI: https://doi.org/10.1007/s00010-014-0309-z