In this paper, we generalize the Takagi function which is known as a nowhere differentiable continuous function, and we clarify the close relation between the Takagi function and Lebesgue's singular function with de Rham's functional equation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.