Abstract
Recently in some considerations connected with the distributivity laws of fuzzy implications over triangular norms and conorms, the following functional equation appeared ƒ(min(x + y, a)) = min(ƒ(x) + ƒ(y), b), (1) where a; b are finite or infinite nonnegative constants (see [1]). In [2] we considered a generalized version of this equation in the case when both a and b are finite, namely the equation ƒ(m 1 (x + y)) = m 2 (ƒ(x) + ƒ(y)), where m 1 , m 2 are functions defined on some finite intervals of ℝ satisfying additional assumptions. In this article we enhance the results from [2], [3] and consider generalized versions of the equation (1) in the cases when a or b is infinite. We show that some well known solutions of several functional equations, that we presented earlier in [1], [4], can be obtained as corollaries of these new facts.
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