Simple Fixed Point Theorems on Linear Continua

  • Jan Andres Dept. of Math. Analysis, Faculty of Science, Palack´y University, Tomkova 40, 779 00 Olomouc-Hejc´ın, Czech Republic.
  • Karel Pastor Dept. of Math. Analysis, Faculty of Science, Palack´y University, Tomkova 40, 779 00 Olomouc-Hejc´ın, Czech Republic.
  • Pavla Snyrychov´a Dept. of Math. Analysis, Faculty of Science, Palack´y University, Tomkova 40, 779 00 Olomouc-Hejc´ın, Czech Republic.
Keywords: Fixed point, periodic orbit, linear continuum, multivalued map, iterates, connected graph, period implications

Abstract

A simple fixed point theorem is formulated for multivalued maps with a connected graph on closed intervals of linear continua. These intervals either cover themselves or are concerned with self-maps. We discuss a question when the original map can possess a fixed point, provided the same assumptions are satisfied only for some of its iterate. We are particularly interested in a situation on noncompact connected linearly ordered spaces. Many illustrating examples are supplied.

Published
2008-12-01
How to Cite
[1]
J. Andres, K. Pastor, and Snyrychov´aP., “Simple Fixed Point Theorems on Linear Continua”, CUBO, vol. 10, no. 4, pp. 27–43, Dec. 2008.