Vol. 68, No. 1, 1977

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ISSN: 0030-8730
Iterations and fixpoints

Benno Fuchssteiner

Vol. 68 (1977), No. 1, 73–80
Abstract

Starting with a decreasing map φ : X X on a partially ordered set X we construct a map It φ which intuitively can be understood as the iteration (countable or transfinite) of φ. The main properties which It φ inherits from φ are investigated. As application of the main result some fixpoint theorems are proved. Besides, our method yields constructive proofs for results which are usually demonstrated with the help of the axiom of choice.

Mathematical Subject Classification 2000
Primary: 47H10
Milestones
Received: 16 November 1976
Published: 1 January 1977
Authors
Benno Fuchssteiner