A Note on Discontinuous Functions with Continuous Second Iterate

This paper investigates four classes of functions with a single discontinuous point. We give the sufficient and necessary conditions under which the second order iterates are continuous functions. Furthermore, the sufficient conditions for the continuity of the even order iterates with finitely many discontinuous points are obtained.

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Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Zhang, P. and Gong, X. (2015) A Note on Discontinuous Functions with Continuous Second Iterate. Journal of Applied Mathematics and Physics, 3, 691-696. doi: 10.4236/jamp.2015.36082.

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