Let $P$ be a cone in a Hilbert space $H$, $A: P\rightarrow 2^P$ be an accretive mapping (equivalently, $-A$ be a dissipative mapping) and $T:P\rightarrow P$ be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type $-A+T$ are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in $L^2(\Omega)$.
@article{118983,
author = {Shih-sen Chang and Yu-Qing Chen and Yeol Je Cho and Byung-Soo Lee},
title = {Fixed point theorems for nonexpansive operators with dissipative perturbations in cones},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {39},
year = {1998},
pages = {49-54},
zbl = {0937.47053},
mrnumber = {1622324},
language = {en},
url = {http://dml.mathdoc.fr/item/118983}
}
Chang, Shih-sen; Chen, Yu-Qing; Cho, Yeol Je; Lee, Byung-Soo. Fixed point theorems for nonexpansive operators with dissipative perturbations in cones. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 49-54. http://gdmltest.u-ga.fr/item/118983/
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