Abstract
Starting from the classical Weierstrass functions, in this chapter we introduce the so-called Weierstrass functions of max-product type, for which we prove that the set of the points of non-differentiability is uncountable, nowhere dense and of Lebesgue measure 0. Also, the fractal properties of these functions are studied.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hardy, G.H.: Weierstrass’s non-differentiable function. Trans. Am. Math. Soc. 17 (3), 301–325 (1916)
Przytycki F., Urbański, M.: On the Hausdorff dimension of some fractal sets. Stud. Math. 93, 155–186 (1989)
Yamaguti, M., Hata, M., Kigami, J.: Mathematics of Fractals. Translations of Mathematical Monographs, vol. 167. American Mathematical Society, Providence (1993)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bede, B., Coroianu, L., Gal, S.G. (2016). Max-Product Weierstrass Type Functions. In: Approximation by Max-Product Type Operators. Springer, Cham. https://doi.org/10.1007/978-3-319-34189-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-34189-7_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-34188-0
Online ISBN: 978-3-319-34189-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)