On one fractal property of the Minkowski function

DOI10.1007/S13398-017-0396-5zbMath1387.28013arXiv1701.06640OpenAlexW2580962827MaRDI QIDQ1742922

Symon Serbenyuk

Publication date: 12 April 2018

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.06640

zbMATH Keywords

singular functionfractalHausdorff-Besicovitch dimensionself-similar setMinkowski function

Mathematics Subject Classification ID

Singular functions, Cantor functions, functions with other special properties (26A30) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80) Metric theory of continued fractions (11K50)

Related Items (10)

Systems of functional equations and generalizations of certain functions ⋮ One distribution function on the Moran sets ⋮ A certain modification of classical singular function ⋮ On certain maps defined by infinite sums ⋮ Functional equations, alternating expansions, and generalizations of the Salem functions ⋮ The generalized Salem functions defined in terms of certain Cantor expansions ⋮ Relationships between singular expansions of real numbers ⋮ Generalizations of certain representations of real numbers ⋮ Certain singular distributions and fractals ⋮ Some fractal properties of sets having the Moran structure

Cites Work

• Unnamed Item
• Continued fraction Cantor sets, Hausdorff dimension, and functional analysis
• A PROBLEM IN THE FRACTIONAL DIMENSION THEORY OF CONTINUED FRACTIONS

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