Set-valued functions / Funções ponto a conjunto

AUTOR(ES)
DATA DE PUBLICAÇÃO

2005

RESUMO

We study a mapping called a set-valued map which associates with each point of a metric space a non empty subset of another metric space. In the case of single-valued maps, contin-uous functions are characterized by two equivalent properties: one in terms of neighborhood and other in terms of sequences. These two properties can be adapted to the case of set-valued maps, are no longer equivalent and are called upper semi continuity and lower semi continuity, respectively. We adapt to the set-valued case the concept of Lipschitz applications and also a type of continuity when the range is enjoyed with the Hausdorff metric. We related them with the conditions of semi continuity. Some of the results depends on algebraic or topological prop-erties of the images. We adapt to closed convex process the principIe of uniform boundedness, the Banach open mapping and closed graph theorems. The closed convex processes are the set-valued analogues of continuous linear operators. We also establish two fixed point result for set-valued maps: the first generalizes the Schauder fixed point theorem and the second considers that of contraction type

ASSUNTO(S)

teoria da aproximação funções de conjuntos functional analysis analise funcional set-valued functions approximation theory

ACESSO AO ARTIGO

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