TITLE:
A Note on Discontinuous Functions with Continuous Second Iterate
AUTHORS:
Pingping Zhang, Xiaobing Gong
KEYWORDS:
Iteration, Discontinuous Point, Continuous Function
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.6,
June
30,
2015
ABSTRACT: 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.