Year: 2013
Analysis in Theory and Applications, Vol. 29 (2013), Iss. 3 : pp. 208–220
Abstract
In this work, using an analogue of Sadovskii's fixed point result and several important inequalities we investigate and give new existence theorems for the nonlinear operator equation $F(x)=\mu x$, $(\mu \geq 1)$ for some weakly sequentially continuous, weakly condensing and weakly $1$-set weakly contractive operators with different boundary conditions. Correspondingly, we can obtain some applicable fixed point theorems of Leray-Schauder, Altman and Furi-Pera types in the weak topology setting which generalize and improve the corresponding results of [3,15,16].
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2013.v29.n3.2
Analysis in Theory and Applications, Vol. 29 (2013), Iss. 3 : pp. 208–220
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Weakly condensing weakly sequentially continuous fixed point theorem operator equation.