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Self-similar functions, fractals and algebraic genericity

Authors: D. Cariello, V. V. Fávaro and J. B. Seoane-Sepúlveda
Journal: Proc. Amer. Math. Soc. 145 (2017), 4151-4159
MSC (2010): Primary 15A03, 26A15
Published electronically: April 4, 2017
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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce the class of everywhere like functions, which helps us to recover some known classes (such as that of everywhere surjective ones). We also study the algebraic genericity of this new class together with the class of fractal functions.

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Additional Information

D. Cariello
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Plaza de Ciencias 3, Universidad Complutense de Madrid, Madrid, 28040, Spain — and — Faculdade de Matemática, Universidade Federal de Uberlândia, 38.400-902, Uberlândia, Brazil

V. V. Fávaro
Affiliation: Faculdade de Matemática, Universidade Federal de Uberlândia, 38.400-902 Uberlândia, Brazil

J. B. Seoane-Sepúlveda
Affiliation: Departamento de Análisis Matemático, Instituto de Matemática Interdisciplinar, Facultad de Ciencias Matemáticas, Plaza de Ciencias 3, Universidad Complutense de Madrid, Madrid, 28040, Spain

Keywords: Lineability, spaceability, everywhere surjective function, fractal, Darboux.
Received by editor(s): August 30, 2016
Received by editor(s) in revised form: October 24, 2016
Published electronically: April 4, 2017
Additional Notes: The first author was supported by CNPq-Brazil Grant 245277/2012-9
The second author was supported by FAPEMIG Grant PPM-00086-14 and CNPq Grants 482515/2013-9, 307517/2014-4
The third author was supported by MTM2015-65825-P
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society

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