Functional equations generating space-densifying curves

DOI10.1016/S0898-1221(00)00085-7zbMath0954.39016OpenAlexW2052332777MaRDI QIDQ1569983

Gaspar Mora, Abdelkader Ziadi, Yves Cherruault

Publication date: 20 September 2000

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(00)00085-7

zbMATH Keywords

continuous solutionsfunctional equationsadditive functionsspace-filling curvesHamel basesnoncontinuous solutionsspace densifying

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Singular functions, Cantor functions, functions with other special properties (26A30) Functional equations for real functions (39B22) Functional equations for functions with more general domains and/or ranges (39B52) Functional equations for complex functions (39B32)

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Cites Work

• Space-filling curves
• Characterization and generation of \(\alpha\)-dense curves
• An approximation method for the optimization of continuous functions ofnvariables by densifying their domains
• The theoretic calculation time associated to α‐dense curves
• Generation of α‐dense curves in a cube of IRⁿ
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