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