IJPAM: Volume 54, No. 3 (2009)

TAKAGI'S FUNCTION REVISITED FROM
AN ARITHMETICAL POINT OF VIEW

E. de Amo$^1$, J. Fernández-Sánchez$^2$
$^{1,2}$Department of Algebra and Mathematical Analysis
University of Almería
Almería, 04120, SPAIN
$^1$e-mail: [email protected]


Abstract.We revisite Takagi's peculiar function $T$ 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 $T$, 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
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 3