On some conditional functional equations of Gołąb-Schinzel type
We consider equation (6) in the class of continuous functions f: I→ℝ satisfying (7), where f is a non-trivial real interval and n,k are fixed positive integers. The obtained results are applied to get the solutions of the system of functional equations (3)-(5) in the class of pairs of functions f,g: I→ℝ such that f is continuous. Some connections between solutions of the equations and a class of subsemigroups of some Lie groups are established as well.
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