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
Andres, J., Pastor, K., & Snyrychov´aP. (2008). Simple Fixed Point Theorems on Linear Continua. CUBO, A Mathematical Journal, 10(4), 27–43. Retrieved from http://revistas.ufro.cl/ojs/index.php/cubo/article/view/1486