A family of singular functions and its relation to harmonic fractal analysis and fuzzy logic

• Autorzy: Enrique de Amo , Manuel Díaz Carrillo , Juan Fernández-Sánchez
• Języki publikacji: EN

Abstrakty

EN

We study a parameterized family of singular functions which appears in a paper by H. Okamoto and M. Wunsch (2007). Various properties are revisited from the viewpoint of fractal geometry and probabilistic techniques. Hausdorff dimensions are calculated for several sets related to these functions, and new properties close to fractal analysis and strong negations are explored.

Słowa kluczowe

EN

Singular function; Hausdorff dimension; Katok foliation; Strong negation

Kategorie tematyczne

• 26A48: Monotonic functions, generalizations
• 11A67: Other representations
• 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
• 26A30: Singular functions, Cantor functions, functions with other special properties

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 1039-1052

Daty

wydano

2016-01-01

otrzymano

2016-07-28

zaakceptowano

2016-11-08

online

2016-12-17

Twórcy

autor

Enrique de Amo

• Departamento de Matemáticas, Universidad de Almeía,

autor

Manuel Díaz Carrillo

• Departamento de Análisis Matemático, Universidad de Granada,

autor

Juan Fernández-Sánchez

• Grupo de Investigación de Análisis Matemático, Universidad de Almería,

Identyfikatory

DOI

10.1515/math-2016-0094