On fixed points of some functions


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	On fixed points of some functions


	Fixed Point Theory, Volume 20, No. 2, 2019, 507-510, June 1st, 2019 DOI: 10.24193/fpt-ro.2019.2.32 Authors: Zbigniew Grande Abstract: Let ƒ:[0,1] → [0,1] be a Darboux function of Baire class one. Then ƒ has fixed point x ∈ [0,1], ie. there is a point x ∈ [0,1] such that ƒ(x) = x. So approximate continuity of ƒ implies that ƒ has a fixed point. In this article I investigate when ƒ has a fixed point x satisfying some other conditions (for example ƒ is bilaterally quasicontinuous at x or even continuous at x). Key Words and Phrases: Darboux property, Baire class 1, density topologies, quasi-continuity. 2010 Mathematics Subject Classification: 26A05, 26A15, 28A05. Published on-line: June 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents