Licenciatura em Matemática (Sede)
URI permanente desta comunidadehttps://arandu.ufrpe.br/handle/123456789/24
Siglas das Coleções:
APP - Artigo Publicado em Periódico
TAE - Trabalho Apresentado em Evento
TCC - Trabalho de Conclusão de Curso
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4 resultados
Resultados da Pesquisa
Item Pontos fixos em espaços métricos completos e o Teorema de Picard(2023-09-21) Lima, Ana Catarine Freitas de; Carvalho, Gilson Mamede de; http://lattes.cnpq.br/0044877127514130; http://lattes.cnpq.br/8761735112729494This work aims to deepen the study of complete metric spaces, focusing especially on the analysis of fixed points. Our intention is to demonstrate Banach’s Fixed Point Theorem and, subsequently, apply this theory to ordinary differential equations through Picard’s Theorem. To achieve this objective, we will begin by addressing the fundamental concepts of metric spaces, with an emphasis on understanding the basic elements , offering examples and introducing topological concepts, as well as the notion of continuity. We will conduct the study until we reach the definition of complete metric spaces, and then analyze the notion of fixed point. Finally, we will demonstrate the main theorem, which establishes the existence and uniqueness of solutions to initial value problems in ordinary differential equations.Item Sobre uma família de equações de Volterra provenientes da teoria viscoelástica(2021-07-23) Silva, Matheus Henrique Severino da; Silva, Clessius; http://lattes.cnpq.br/2401078773322406; http://lattes.cnpq.br/0142680745727308Using Functional Analysis and Topology tools, we study equations that describe the velocity field of a three-dimensional incompressible, homogeneous, isotropic viscoelastic fuid. To guarantee the existence and mild solution of the proposed problem, the behavior of the solving family associated with the Stokes operator in fractional power spaces was studied.Item Um estudo sobre completude e compacidade em espaços métricos(2019-12-18) Silva, Hugo Henryque Coelho e; Araújo, Yane Lísley Ramos; http://lattes.cnpq.br/6642941380570085; http://lattes.cnpq.br/1324983852661350In this work we will present a study about the theory of complete and compact metric spaces. Initially, we will cover some basic concepts related to the theory of metric spaces, continuity and sequences in metric spaces. Next, we will list a motivation for the study of the theory of complete metric spaces, some of their properties and valid results in these spaces, such as Baire’s theorem and Banach’s fixed point theorem as well as some of its applications. Finally, we will present a study about the theory of compact metric spaces, addressing its general properties and some important results of the mathematical analysis that are valid in these spaces, as we can mention Riesz theorem and Ascoli-Arzelá theorem.Item A compacidade em alguns universos topológicos(2021-07-13) Lima, Alexandre César Bispo; Carvalho, Gilson Mamede de; http://lattes.cnpq.br/0044877127514130; http://lattes.cnpq.br/4592972030162451This work aims to study and establish relationships between compact sets and topology, emphasizing the compactness of the unitary closed ball in different contexts. For this, initially we dealt with topological spaces in Chapter 1, we developed basic concepts and tools that will be useful until we get to the central theme of compactness. Then, in Chapter 2, we focus the study on the more particular environment of metric spaces, where we develop the concepts and results in order to end the chapter with a compactness characterization of the unitary closed ball of space. Finally, in Chapter 3, we study how weak and weak* topologies, drawing as a final result the famous Banach- Alaoglu-Bourbaki Theorem, which tells us that the unitary closed ball in the topological dual of a space of Banach is weak* compact.