A Conjectura do quociente separável, uma conjectura sobre EDO's em espaços de Banach, uma teoria de aproximação de pontos fixos, e contribuições

• Ano de defesa: 2012
• Autor(a) principal: Rebouças, Michel Pinho
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Análise matemática; Banach, espaços de
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/4539

We establish some results concerning the Cauchy-Peano problem in Banach spaces, the separable quotient problem and the approximate fixed point theory. We prove that a Banach space E contains a nontrivial separable quotient if it's dual admits a weak*-transfinite Schauder frame. Next, we study a kind of algebraic genericity for the weak form of Peano's theorem in Banach spaces having complemented subspaces with unconditional Schauder basis. Moreover, we introduce and study a notion of weak-approximate solutions for the non-autonomous Cauchy-Peano problem in Banach spaces. It's proved that the absence of ℓ1-isomorphs inside the space is equivalent to the existence of weak-approximate fixed point theory. Firstly, we study some relationships between biorthogonal systems, linear topologies and the weak-approximate fixed point property. After, we establish some optimal approximate fixed point results in locally convex spaces.