On the sets of fixed points of bounded Baire one functions

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 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.

Original languageEnglish (US)
Article number1950040
JournalAsian-European Journal of Mathematics
Volume12
Issue number3
DOIs
StatePublished - Jun 1 2019

Fingerprint

Fixed point
Borel Measure
Closed
Interval
Unit
Arbitrary
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{a1751c7c25cd42f988f508e93b73d085,
title = "On the sets of fixed points of bounded Baire one functions",
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 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.",
author = "Aliasghar Alikhani-Koopae",
year = "2019",
month = "6",
day = "1",
doi = "10.1142/S1793557119500402",
language = "English (US)",
volume = "12",
journal = "Asian-European Journal of Mathematics",
issn = "1793-5571",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "3",

}

On the sets of fixed points of bounded Baire one functions. / Alikhani-Koopae, Aliasghar.

In: Asian-European Journal of Mathematics, Vol. 12, No. 3, 1950040, 01.06.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the sets of fixed points of bounded Baire one functions

AU - Alikhani-Koopae, Aliasghar

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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 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.

AB - 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 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.

UR - http://www.scopus.com/inward/record.url?scp=85047817823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047817823&partnerID=8YFLogxK

U2 - 10.1142/S1793557119500402

DO - 10.1142/S1793557119500402

M3 - Article

VL - 12

JO - Asian-European Journal of Mathematics

JF - Asian-European Journal of Mathematics

SN - 1793-5571

IS - 3

M1 - 1950040

ER -