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Mathematical Analysis Fundamentals by Agamirza Bashirov

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image
Figure 7.5 Proof of Theorem 7.24.

Note that Theorem 7.24 states only the existence of a solution of the differential Eq. (7.11) if fimage is continuous. For uniqueness of the solution, we need a stronger condition. This subject will be handled later (see Theorem 9.30).

7.7* Banach Spaces and the Space C1(a,b)image

In this section we are looking to a suitable structure for a subset of C(a,b), consisting of all differentiable functions with continuous derivatives ...

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