On the superstability of generalized d’Alembert harmonic functions
2016 ◽
Vol 15
(1)
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pp. 5-13
Keyword(s):
AbstractThe aim of this paper is to study the superstability problem of the d’Alembert type functional equation $$f(x + y + z) + f(x + y + \sigma (z)) + f(x + \sigma (y) + z) + f(\sigma (x) + y + z) = 4f(x)f(y)f(z)$$ for all x, y, z ∈ G, where G is an abelian group and σ : G → G is an endomorphism such that σ(σ(x)) = x for an unknown function f from G into ℂ or into a commutative semisimple Banach algebra.
1952 ◽
Vol 63
(4)
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pp. 336-345
1997 ◽
Vol 63
(3)
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pp. 289-296
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1996 ◽
Vol 120
(3)
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pp. 455-473
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Keyword(s):
2013 ◽
Vol 2
(1)
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Keyword(s):