The Fixed Point Property For Closed Neighborhoods of Line Segments In L^P

Authors

Bernd Schroeder, University of Southern MississippiFollow

Document Type

Article

Publication Date

1-1-2019

Department

Mathematics

School

Mathematics and Natural Sciences

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 inL¹ has a fixed point.

Publication Title

Fixed Point Theory

Volume

20

Issue

1

First Page

299

Last Page

321

Recommended Citation

Schroeder, B. (2019). The Fixed Point Property For Closed Neighborhoods of Line Segments In L^P. Fixed Point Theory, 20(1), 299-321.
Available at: https://aquila.usm.edu/fac_pubs/18059