On Fixed Points of Locally and Pointwise Contractive Set-Valued Maps

Loch-Temzelides, Ted2022-09-132022-09-132022-06https://hdl.handle.net/11299/241544University of Minnesota M.S. thesis. June 2022. Major: Mathematics. Advisor: Peter Olver. 1 computer file (PDF); v, 58 pages.Generalizations of Banach's (1922) contraction mapping theorem for single-valued maps satisfying pointwise or local contraction properties require additional restrictions on the underlying metric space. Using a Hausdorff metric, this paper establishes conditions under which pointwise or local contraction properties imply the existence of fixed points for set-valued maps.encontraction mappingFixed pointsSet-valued mapsOn Fixed Points of Locally and Pointwise Contractive Set-Valued MapsThesis or Dissertation