Az Egri Ho Si Minh Tanárképző Főiskola Tud. Közleményei. 1987. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 18/11)
Szepessy Bálint: Megjegyzések a valós függvények iterálásához IV
- 41 SZEPESSY BÁLINT MEGJEGYZÉSEK A VALÓS FÜGGVÉNYEK ITERÁLÁSÁHOZ IV. (A negyedrendű ciklusokról) Abstract: (Remarks on iteration of real functions IV.) A real valued function f(x), defined on the closed interval [a,b], is called iterational basic function if (i) f(x) is a continuous function at every inside points of the interval [a, b] ; furthermore f(x) is continuous on the right and on the left at point a and b respectively; (ii) f(x) maps the interval [ a, bJ onto itself; (iii) there is no subinterval of the interval [ a,b] where f(x) is a constant function; For i=0,l,2,... the function f.Cx), defined by f QCx)=x and f . <x)=f [f . for i > 0; is called i t h iterated function of f(x). We say a real number c is a fix point of f(x) of order one if f(c)=c, furthermore c is a fix point of order r if f (c)=c but f n<c>i*c for n=l,2, ,r-l. If c is a fix point of f(x) of order r, then the numbers fj« 3}™ 0*» f ( ci] = c2' * * * » r [ c r-i] = c are also fix points of order r and the fix points c 1,c , give a cycle of order r. In some earlier papers we gave conditions for f(x) if it has no fix point
