On a flexible class of continuous functionswith uniform local structur

摘要

This paper considers a class of continuous functions constructed asa series of iterates of the "tent map" multiplied by variable signs. This class includesTakagi's nowhere-differentiable function, and contains the functions studied by Hataand Yamaguti Japan J. Appl. Math., 1 (1984), 183-199 and Kono Acta Math.Hungar., 49 (1987), 315-324 as a proper subclass. A complete description is givenof the differentiability properties of the functions in this class, and several statementsare proved concerning their uniform and local moduli of continuity. The results areapplied to generation of random functions.