PM functions, their characteristic intervals and iterative roots

• Autorzy: Weinian Zhang
• Języki publikacji: EN

Abstrakty

EN

The concept of characteristic interval for piecewise monotone functions is introduced and used in the study of their iterative roots on a closed interval.

Słowa kluczowe

EN

iterative root; piecewise monotone function; characteristic interval

Kategorie tematyczne

• 39B12: Iteration theory, iterative and composite equations
• 39B22: Equations for real functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996-1997
• Tom: 65
• Numer: 2
• Strony: 119-128

Daty

wydano

1997

otrzymano

1994-11-14

poprawiono

1995-09-11

Twórcy

autor

Weinian Zhang

• Centre for Math. Sciences, CICA, Academia Sinica, Chengdu 610041, P.R. China

Bibliografia

• [1] N. H. Abel, Oeuvres Complètes, t. II, Christiania, 1881, 36-39.
• [2] U. T. Bödewadt, Zur Iteration reeller Funktionen, Math. Z. 49 (1944), 497-516.
• [3] J. M. Dubbey, The Mathematical Work of Charles Babbage, Cambridge Univ. Press, 1978.
• [4] M. K. Fort Jr., The embedding of homeomorphisms in flows, Proc. Amer. Math. Soc. 6 (1955), 960-967.
• [5] H. Kneser, Reelle analytische Lösungen der Gleichung $φ(φ(x)) = e^x$ und verwandter Funktionalgleichungen, J. Reine Angew. Math. 187 (1950), 56-67.
• [6] G. Koenigs, Recherches sur les intégrales de certaines équations fonctionnelles, Ann. Ecole Norm. Sup. (3) 1 (1884), Suppl., 3-41.
• [7] M. Kuczma, Functional Equations in a Single Variable, Monografie Mat. 46, PWN, Warszawa, 1968.
• [8] M. Kuczma, Fractional iteration of differentiable functions, Ann. Polon. Math. 22 (1969/70), 217-227.
• [9] M. Kuczma and A. Smajdor, Fractional iteration in the class of convex functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 717-720.
• [10] R. E. Rice, B. Schweizer and A. Sklar, When is f(f(z)) = az²+bz+c?, Amer. Math. Monthly 87 (1980), 252-263.
• [11] J. Zhang and L. Yang, Discussion on iterative roots of piecewise monotone functions, Acta Math. Sinica 26 (1983), 398-412 (in Chinese).