Limit oscillations of locally stable functions

Maslyuchenko Oleksandr Volodymyrovych; Onypa Denys Pavlovich

Maslyuchenko Oleksandr Volodymyrovych ^1,2 , Onypa Denys Pavlovich ²

¹ Institute of Mathematics, University of Silesia in Katowice, Katowice, 40-007, Poland

² Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: limit oscillations, nonnegative continuous function

Download

Abstract

In this paper we prove that every nonnegative continuous function defined on a closed nowhere dense subset of the reals without isolated points is the limiting oscillation of some locally constant function defined on the complement to this set.

References

[1] Kostyrko P. Some properties of oscilation // Math. Slovaca. – 1980. – 30. – P.157–162.

[2] Duszynski Z. On the $ω$–primitives // Math.Slovaka. – 2001. – 51 . – P.469–476.

[3] Ewert J., Ponomarev S. Oscillation and $ω$–primitives // Real Anal. Exchange. – 2001–2002. – 26 . – P. 687–702.

[4] Ewert J., Ponomarev S. On the existance of $ω$-primitives on arbitrary metric spaces // Math. Slovaca. – 2003. – 53 . – P.51–57.

[5] Maslyuchenko O.V. Construction of $ω$-firsts and various analogues of compact operators: PhD in Physics and Mathematics: 01.01.01. - Chernivtsi, 2012. - 300 p.

[6] Maslyuchenko O.V. The oscillation of quasicontinuous functions on pairwise attainable spaces // Houston Journal of Mathematics. 2009. - 35 , N1. - P.113-130.

[7] Maslyuchenko O.V. Construction of $ω$-primaries: oscillations of the sum of functions // Mathematical Bulletin of the National Academy of Sciences. - 5. - 2008. - P.151-163.

[8] Maslyuchenko O.V. Construction of $ω$-primary: strongly attainable spaces // Mathematical Bulletin of the National Academy of Sciences. - 6. - 2009. - P.155-178.

[9] Maslyuchenko O.V. Oscillations of nonlinearly locally Lipschitz functions // Carpathian mathematical publications.2011.- 3, N1.- P.22-33.

[10] Engelking R. General Topology // Moscow: Mir, 1986. - 752 p.

Download

Cite

ACS Style: Maslyuchenko, O.V.; Onypa, D.P. Limit oscillations of locally stable functions. Bukovinian Mathematical Journal. 2016, 1
AMA Style: Maslyuchenko OV, Onypa DP. Limit oscillations of locally stable functions. Bukovinian Mathematical Journal. 2016; 1(3-4).
Chicago/Turabian Style: Oleksandr Volodymyrovych Maslyuchenko, Denys Pavlovich Onypa. 2016. "Limit oscillations of locally stable functions". Bukovinian Mathematical Journal. 1 no. 3-4.

Export

BibTex EndNote RIS