The Fixed Point Property For Closed Neighborhoods of Line Segments In LP
Mathematics and Natural Sciences
We prove that, in Lp-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.
Fixed Point Theory
(2019). The Fixed Point Property For Closed Neighborhoods of Line Segments In LP. Fixed Point Theory, 20(1), 299-321.
Available at: https://aquila.usm.edu/fac_pubs/18059