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Proceedings of the American Mathematical Society

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On the roots of equation $ f(x)=\xi$ where $ f(x)$ is real and continuous in $ (a,b)$ but monotonic in no subinterval of $ (a,b)$

Author: K. Padmavally
Journal: Proc. Amer. Math. Soc. 4 (1953), 839-841
MSC: Primary 27.2X
MathSciNet review: 0059341
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References [Enhancements On Off] (What's this?)

  • [1] Alfred Köpcke, Ueber eine durchaus differentiirbare, stetige Function mit Oscillationen in jedem Intervalle, Math. Ann. 34 (1889), no. 2, 161–171 (German). MR 1510572,
  • [2] S. Minakshisundaram, On the roots of a continuous non-differentiable function, J. Indian Math. Soc. (N.S.) 4 (1940), 31–33. MR 0001827
  • [3] T. Radó, Length and area, Amer. Math. Soc. Colloquium Publications, vol. 30, 1948, p. 193.
  • [4] A. N. Singh, Theory and construction of non-differentiable functions, p. 89.

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