IJPAM: Volume 54, No. 3 (2009)
AN ARITHMETICAL POINT OF VIEW
Department of Algebra and Mathematical Analysis
University of Almería
Almería, 04120, SPAIN
Abstract.We revisite Takagi's peculiar function with the aid of arithmetical techniques (instead of the more known geometrical ones). This formula simplyfies computations, and classical properties are now easily derived from it.
Among the other results, Kono's Probability Theorem, functional equations
characterasing , and Trollope summation formula are newly shown.
Received: June 27, 2009
AMS Subject Classification: 26A09, 26A06, 26A27
Key Words and Phrases: binary expansions, (local) Lipschitz condition, Hölder continuity, fixed point Banach's Theorem, Schauder's basis, selfsimilarity, fractal dimension
Source: International Journal of Pure and Applied Mathematics