Fixed points and iteration homotopies

Francis J. Papp
1972 Journal of the Australian Mathematical Society  
Communicated by B. Mond Suppose that 0 is a topological space equipped with a Hausdorff topology and that T is a continuous function mapping $ into , t) of $ x [0, 1] to # will be called an iteration homotopy for T if i) H T ((f), t) is a homotopy ii) there exists a strictly decreasing sequence {n s \s -1, 2, • • •} of points in [0, 1 ] for which: a) Wl = 1 b) H T (,n s ) = T s , where T s = T{r~l4), s = 2, 3, • • • c) lim n s = 0. S-+0O THEOREM 2. A function T has at most one fixed point if i)
more » ... e fixed point if i) an iteration homotopy for T exists, and ii) H T (, 0) has at most one fixed point.
doi:10.1017/s1446788700010557 fatcat:inqg6igeevavtm4ia24x2gicg4