Anal. Theory Appl., 29 (2013), pp. 208-220.
Published online: 2013-07
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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].
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n3.2}, url = {http://global-sci.org/intro/article_detail/ata/5058.html} }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].