Nondifferentiable Functions

  • Palaniappan Kannappan
Part of the Springer Monographs in Mathematics book series (SMM)


Nondifferential functions, Weierstrass functions, Vander Waerden type functions, and generalizations are considered in this chapter. In classical analysis, one of the problems that has fascinated mathematicians since the end of the nineteenth century is ‘Does there exist a continuous function that is not differentiable?’ It is an interesting question. Motivated by this exciting question, many well-known mathematicians, starting with Weierstrass (1872) [827], started to work in this area to produce such a function. It is well known that the answer is affirmative. This chapter is devoted to listing several continuous non- (nowhere) differentiable functions (c.n.d.f.s). What is of interest to us and is the primary motive of this chapter is to show that most of the well-known examples can be obtained as solutions of functional equations, highlighting the functional equation connection. Kairies’s [412] report is an excellent survey article and a main source for this chapter.


Functional Equation Iterative Equation Weierstrass Function Nondifferentiable Function Unique Continuous Solution 
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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterloo ONCanada

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