Continuous Nowhere Differentiable Functions by Marek Jarnicki & Peter Pflug

Author:Marek Jarnicki & Peter Pflug
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(8.4.4)

with the associated data , , and , , . Then f is the uniquely determined solution of the following system:

(8.4.5)

where and , .

By virtue of Theorem 8.4.12, it suffices to find suitable indices i, j, n such that , where the data δ i, j, n (f) and are taken with respect to the system (8.4.5).

By virtue of Theorem 8.4.4, it is clear that

where is understood with respect to (8.4.4). Moreover,

where is understood with respect to (8.4.4).

Now fix the indices i 0 = 0, j 0 = b − 1, and n 0 = 2. Then Theorem 8.4.9 leads to

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