The fixed point property for closed neighborhoods of line segments in Lp


	Open access
	The fixed point property for closed neighborhoods of line segments in L^p


	Fixed Point Theory, Volume 20, No. 1, 2019, 299-322, February 1st, 2019 DOI: 10.24193/fpt-ro.2019.1.20 Authors: Bernd S.W. Schröder Abstract: We prove that, in L^p-spaces with p ∈ (1, ∞], closed neighborhoods of line segments are dismantlable and hence every monotone operator on these neighborhoods has a fixed point. We also give an example that, for p = 1, closed neighborhoods of line segments need not be dismantlable. It is an open question whether every monotone self map of a closed neighborhood of a line segment in L¹ has a fixed point. Key Words and Phrases: Dismantlable ordered set, fixed point property, line segment, closed L^p-neighborhood. 2010 Mathematics Subject Classification: 06A07, 46B42, 47H07, 47H10. Published on-line: February 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents