Multivariable Dynamic Calculus on Time Scales by Martin Bohner & Svetlin G. Georgiev

Author:Martin Bohner & Svetlin G. Georgiev
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Problem 4.52

Using Theorem 4.32, prove that the following series are uniformly convergent.

1. , ,

2. , ,

3. , ,

4. , ,

5. , ,

6. , .

Problem 4.53

Using the Abel test, prove that the series

is uniformly convergent on .

Problem 4.54

Let . Using the Dirichlet test, prove that

is uniformly convergent on .

4.4 Notes and References

In this chapter, the concept of function series and sequences is extended to time scales. Necessary and sufficient conditions and several criteria for uniform convergence of function series and sequences are presented. Several analytical properties of function series and function sequences on general time scales are given. All results in this chapter are taken from Pang and Wang [36].

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