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 (piecewise continuous, continuous, smooth)
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