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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A monotonicity theorem for the family $f_{a}(x)=a-x^{2}$
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by Leo Jonker PDF
Proc. Amer. Math. Soc. 85 (1982), 434-436 Request permission

Abstract:

Let ${f_a}(x) = a - {x^2}$, $x \in [ - \tfrac {1} {2} - \tfrac {1} {2}\sqrt {1 + 4a}$, $\tfrac {1} {2} + \tfrac {1} {2}\sqrt {1 + 4a} ]$ and $a \in [0,2]$. It is proved that if ${f_a}$ has a periodic orbit of odd period $n$ and if $b > a$, then ${f_b}$ has a periodic orbit of period $n$. This is equivalent to the corresponding result for the function family ${g_\lambda }(x) = \lambda x(1 - x)$, $x \in [0,1]$, $\lambda \in [0,4]$.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 434-436
  • MSC: Primary 58F20; Secondary 34C25, 54C05
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0656118-0
  • MathSciNet review: 656118