Common fixed points for commuting Cournot maps. (English) Zbl 1049.37034

Linero, A.

Real Anal. Exch. 28(2002-2003), No. 1, 121-143 (2003).

The author studies the existence of common fixed points of two commuting Cournot maps on \([0,1]^2\). Extensions of results by J. R. Jachymski [Proc. Am. Math. Soc. 124, 3229–3233 (1996; Zbl 0881.54043)] and G. F. Jungck [Proc. Am. Math. Soc. 115, 495–499 (1992; Zbl 0771.54037)] to the Cournot case are given.

Reviewer: Klaudiusz Wójcik (Kraków)

MSC:

37E99	Low-dimensional dynamical systems
26A18	Iteration of real functions in one variable
37E05	Dynamical systems involving maps of the interval
37N40	Dynamical systems in optimization and economics
54H25	Fixed-point and coincidence theorems (topological aspects)

Keywords:

commuting functions; periodic points; common fixed point; Cournot maps; Jungck’s theorem

Citations:

Zbl 0881.54043; Zbl 0771.54037