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Uniqueness theorems for a general class of functional equations
Published online by Cambridge University Press: 09 April 2009
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In a previous paper [1] J. Aczél has shown the following
Theorem 1. If in the (closed, half-closed or open, finite or infinite) interval 〈A, B〉and there f, F are there, f F are continuous, F intern (the value F(x, y) lies strictly between x and y) and u → H(u, v, x, y) or v → H(u, v, x, y) are injective (i.e.
or
, then the functional equation (*) with the initial conditions
has at most one solution.
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