Functional equations for peculiar functions
This is a thorough and interesting survey of functional equations which characterize certain everywhere continuous nowhere differentiable functions, strictly monotonic functions with almost everywhere 0 derivatives, replicative functions (cf. \textit{D. E. Knuth} [The art of computer programming, Vol. I. (1968; Zbl 0191.17903)], etc. It concludes with some open problems and with 122 references.
Continuous nowhere differentiable functions
strictly monotonic functions with almost everywhere 0 derivatives
Characterizations by functional equations in a single variable
scientific article; zbMATH DE number 1019195
scientific article