Skip to main content
Log in

Box dimension of the graph of a continuous function: a necessary condition

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

In questa breve nota si dimostra una condizione necessaria che deve essere soddisfatta nei punti di un sottoinsieme denso del suo insieme di definizione da una funzione reale continua di cui sia nota la dimensione frattale del diagramma.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Biacino, L.:Derivatives of fractional order of continuous functions, Ric. DiMat., 53 (2004), 231–254

  2. Biacino, L.: Hausdorff dimension of the diagram of -Holder continuous functions, Ric. Di Mat., 54 (2005), 229–243

    MathSciNet  Google Scholar 

  3. Falconer, K.J.: The Geometry of Fractal Sets. Cambridge University Press (1985)

  4. Falconer, K.J.: Fractal Geometry: Mathematical Foundations and Applications. New York: John Wiley and Sons Ltd. (1990)

    MATH  Google Scholar 

  5. Mattila, P.: Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press (1995)

  6. Kolwankar, K.M., Levy Vhel, J.: Measuring function smoothness with local fractional derivatives, Fract. Calc. Appl. An., 4 (2001), 285–301

    MATH  Google Scholar 

  7. Tricot, C.: Two definitions of fractional dimension, Math. Proc. Cambridge Phil. Soc., 91 (1982), 57–94

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Loredana Biacino.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Biacino, L. Box dimension of the graph of a continuous function: a necessary condition. Rend. Circ. Mat. Palermo 58, 311–317 (2009). https://doi.org/10.1007/s12215-009-0025-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12215-009-0025-z

Keywords

Mathematics Subject Classification (2000)

Navigation