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

Padmavally, K.

doi:10.1090/S0002-9939-1953-0059341-3

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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On the roots of equation $f(x)=\xi$ where $f(x)$ is real and continuous in $(a,b)$ but monotonic in no subinterval of $(a,b)$
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by K. Padmavally PDF

Proc. Amer. Math. Soc. 4 (1953), 839-841 Request permission

References

Alfred Köpcke, Ueber eine durchaus differentiirbare, stetige Function mit Oscillationen in jedem Intervalle, Math. Ann. 34 (1889), no. 2, 161–171 (German). MR 1510572, DOI 10.1007/BF01453433
S. Minakshisundaram, On the roots of a continuous non-differentiable function, J. Indian Math. Soc. (N.S.) 4 (1940), 31–33. MR 1827

Length and area

Theory and construction of non-differentiable functions