A fixed point theorem for a class of differentiable stable operators in Banach spaces

Vadim Azhmyakov

doi:10.1155/FPTA/2006/92429

A fixed point theorem for a class of differentiable stable operators in Banach spaces

Vadim Azhmyakov

Grupo de Investigación en Modelación y Computación Científica

Resultado de la investigación: Contribución a una revista › Artículo › revisión exhaustiva

Resumen

We study Fréchet differentiable stable operators in real Banachspaces. We present the theory of linear and nonlinear stableoperators in a systematic way and prove solvability theorems for operator equations with differentiable expanding operators. In addition, some relations to the theory of monotone operators in Hilbert spaces are discussed. Using the obtained solvability results, we formulate the corresponding fixed point theorem for aclass of nonlinear expanding operators. Copyright © 2006 Vadim Azhmyakov.

Idioma original	Inglés estadounidense
Publicación	Fixed Point Theory and Applications
DOI	https://doi.org/10.1155/FPTA/2006/92429
Estado	Publicada - 30 jun 2006

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10.1155/FPTA/2006/92429

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AB - We study Fréchet differentiable stable operators in real Banachspaces. We present the theory of linear and nonlinear stableoperators in a systematic way and prove solvability theorems for operator equations with differentiable expanding operators. In addition, some relations to the theory of monotone operators in Hilbert spaces are discussed. Using the obtained solvability results, we formulate the corresponding fixed point theorem for aclass of nonlinear expanding operators. Copyright © 2006 Vadim Azhmyakov.

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