Abstract

We study the conditional functional equation: γ ( x + y ) = γ ( x − y ) ⇒ f ( x + y ) = f ( x ) f ( y ) , with a given function γ ; if γ is a norm in a real linear space, then the equation becomes the well-known isosceles orthogonally exponential functional equation. We give the descriptions of its solutions and investigate the stability of it. We also consider the pexiderized version of the equation.

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