PM functions, their characteristic intervals and iterative roots

Weinian Zhang

Annales Polonici Mathematici (1997)

  • Volume: 65, Issue: 2, page 119-128
  • ISSN: 0066-2216

Abstract

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

How to cite

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Weinian Zhang. "PM functions, their characteristic intervals and iterative roots." Annales Polonici Mathematici 65.2 (1997): 119-128. <http://eudml.org/doc/269950>.

@article{WeinianZhang1997,
abstract = {The concept of characteristic interval for piecewise monotone functions is introduced and used in the study of their iterative roots on a closed interval.},
author = {Weinian Zhang},
journal = {Annales Polonici Mathematici},
keywords = {iterative root; piecewise monotone function; characteristic interval; continuous iterative roots},
language = {eng},
number = {2},
pages = {119-128},
title = {PM functions, their characteristic intervals and iterative roots},
url = {http://eudml.org/doc/269950},
volume = {65},
year = {1997},
}

TY - JOUR
AU - Weinian Zhang
TI - PM functions, their characteristic intervals and iterative roots
JO - Annales Polonici Mathematici
PY - 1997
VL - 65
IS - 2
SP - 119
EP - 128
AB - The concept of characteristic interval for piecewise monotone functions is introduced and used in the study of their iterative roots on a closed interval.
LA - eng
KW - iterative root; piecewise monotone function; characteristic interval; continuous iterative roots
UR - http://eudml.org/doc/269950
ER -

References

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  1. [1] N. H. Abel, Oeuvres Complètes, t. II, Christiania, 1881, 36-39. 
  2. [2] U. T. Bödewadt, Zur Iteration reeller Funktionen, Math. Z. 49 (1944), 497-516. Zbl0028.35103
  3. [3] J. M. Dubbey, The Mathematical Work of Charles Babbage, Cambridge Univ. Press, 1978. Zbl0376.01002
  4. [4] M. K. Fort Jr., The embedding of homeomorphisms in flows, Proc. Amer. Math. Soc. 6 (1955), 960-967. Zbl0066.41306
  5. [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. [6] G. Koenigs, Recherches sur les intégrales de certaines équations fonctionnelles, Ann. Ecole Norm. Sup. (3) 1 (1884), Suppl., 3-41. 
  7. [7] M. Kuczma, Functional Equations in a Single Variable, Monografie Mat. 46, PWN, Warszawa, 1968. 
  8. [8] M. Kuczma, Fractional iteration of differentiable functions, Ann. Polon. Math. 22 (1969/70), 217-227. Zbl0185.29403
  9. [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. [10] R. E. Rice, B. Schweizer and A. Sklar, When is f(f(z)) = az²+bz+c?, Amer. Math. Monthly 87 (1980), 252-263. Zbl0441.30033
  11. [11] J. Zhang and L. Yang, Discussion on iterative roots of piecewise monotone functions, Acta Math. Sinica 26 (1983), 398-412 (in Chinese). Zbl0529.39006

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