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Volume 29, Issue 3
Fixed Point Theory for 1-Set Weakly Contractive Operators in Banach Spaces

S. Xu & A. Amar

Anal. Theory Appl., 29 (2013), pp. 208-220.

Published online: 2013-07

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  • 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].

  • AMS Subject Headings

47H10, 47J05, 47J10

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COPYRIGHT: © Global Science Press

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@Article{ATA-29-208, author = {}, title = {Fixed Point Theory for 1-Set Weakly Contractive Operators in Banach Spaces}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {3}, pages = {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].

}, 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} }
TY - JOUR T1 - Fixed Point Theory for 1-Set Weakly Contractive Operators in Banach Spaces JO - Analysis in Theory and Applications VL - 3 SP - 208 EP - 220 PY - 2013 DA - 2013/07 SN - 29 DO - http://doi.org/10.4208/ata.2013.v29.n3.2 UR - https://global-sci.org/intro/article_detail/ata/5058.html KW - Weakly condensing, weakly sequentially continuous, fixed point theorem, operator equation. AB -

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].

S. Xu & A. Amar. (1970). Fixed Point Theory for 1-Set Weakly Contractive Operators in Banach Spaces. Analysis in Theory and Applications. 29 (3). 208-220. doi:10.4208/ata.2013.v29.n3.2
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