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- Title
On the sets of fixed points of bounded Baire one functions.
- Authors
Alikhani-Koopaei, Aliasghar
- Abstract
In this paper, we present some results on typical properties of the sets of fixed points of bounded Baire one functions. In particular, we show that typical elements of a uniformly closed subclass 𝒜 of such class of functions have nowhere dense set of fixed points. We also show that typical elements of the class of bounded Baire one functions have μ [ f − 1 (F (f)) ] = 0 , where μ is an arbitrary continuous Borel measure on the unit interval.
- Subjects
FIXED point theory; DYNAMICAL systems; CONTINUOUS functions; FRACTAL dimensions; REAL numbers
- Publication
Asian-European Journal of Mathematics, 2019, Vol 12, Issue 3, pN.PAG
- ISSN
1793-5571
- Publication type
Article
- DOI
10.1142/S1793557119500402