Any qualifying generator on the non-positive reals extends to a solution of the equation, with explicit closed-form expressions available for continuous strictly monotone generators.
Dhombres,Some aspects of functional equations, Chulalongkorn University Press, Bankok 1970
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Quasi graph-additive functions with a prescribed branch
Any qualifying generator on the non-positive reals extends to a solution of the equation, with explicit closed-form expressions available for continuous strictly monotone generators.