Simple Fixed Point Theorems on Linear Continua

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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.

Keywords

Fixed point , periodic orbit , linear continuum , multivalued map , iterates , connected graph , period implications
  • Jan Andres Dept. of Math. Analysis, Faculty of Science, Palack´y University, Tomkova 40, 779 00 Olomouc-Hejc´Ä±n, Czech Republic.
  • Karel Pastor Dept. of Math. Analysis, Faculty of Science, Palack´y University, Tomkova 40, 779 00 Olomouc-Hejc´Ä±n, Czech Republic.
  • Pavla Snyrychov´a Dept. of Math. Analysis, Faculty of Science, Palack´y University, Tomkova 40, 779 00 Olomouc-Hejc´Ä±n, Czech Republic.
  • Pages: 27–43
  • Date Published: 2008-12-01
  • Vol. 10 No. 4 (2008): CUBO, A Mathematical Journal

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Published

2008-12-01

How to Cite

[1]
J. Andres, K. Pastor, and P. Snyrychov´a, “Simple Fixed Point Theorems on Linear Continua”, CUBO, vol. 10, no. 4, pp. 27–43, Dec. 2008.

Issue

Vol. 10 No. 4 (2008): CUBO, A Mathematical Journal

Section

Articles