Um estudo sobre o teorema de Àrzela-Ascoli
The aim of this paper is to conduct a study about sequences and series of functions, in which the main types of convergence are analyzed. It is also proved the following theorem due to Arzela-Ascoli: Given ffngn, equicontinuous and uniformly bounded sequence of functions, de ned on [a; b], there is...
| Autor principal: | Codognos, Mayara Vendramini |
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| Formato: | Trabalho de Conclusão de Curso (Graduação) |
| Idioma: | Português |
| Publicado em: |
Universidade Tecnológica Federal do Paraná
2020
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| Assuntos: | |
| Acesso em linha: |
http://repositorio.utfpr.edu.br/jspui/handle/1/15860 |
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| Resumo: |
The aim of this paper is to conduct a study about sequences and series of functions, in which the main types of convergence are analyzed. It is also proved the following theorem due to Arzela-Ascoli: Given ffngn, equicontinuous and uniformly bounded sequence of functions, de ned on [a; b], there is a subsequence which converges uniformly. In addition, an application of the previous theorem, which lies in the Calculus of Variations will be also addressed. |
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