ON COMMUTING FUNCTIONS,
Abstract
There is a rather well-known conjecture that if f and g are continuous functions from (0,1) to (0, 1) which commute (i.e., f(g(x)) = g(f(x))), then f and g have a common fixed point. The conjecture is known to be true in some special cases; for example, when f and g are polynomials. H. Cohen has proved the conjecture for the case when f and g have a property he calls fullness. In this memorandum the author generalizes Cohen's theorem to the case when f is full and g is arbitrary. This result is especially interesting because the author assumes a special form for only one of the functions. The methods used seem to be new, and the author feels that further work in this direction may eventually yield a proof of the conjecture in the case when one of the functions is of bounded variation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1964
- Accession Number
- AD0608060
Entities
People
- Jon H. Folkman
Organizations
- RAND Corporation