TY - JOUR
T1 - Fixed Point Theory for 1-Set Weakly Contractive Operators in Banach Spaces
AU - S. Xu & A. Amar
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 - <p style="text-align: justify;">In this work, using an analogue of Sadovskii&#39;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].</p>