Geodesic
Fixed point theorems for nonexpansive operators with dissipative perturbations in cones
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 1, pp. 49-54 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $L^2(\Omega)$.
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 $L^2(\Omega)$.
Classification : 45G10, 45H10, 47H06, 47H09, 47H10, 47H15
Keywords: nonexpansive mapping; accretive mapping; fixed point theorem; nonlinear integral equations 
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     title = {Fixed point theorems for nonexpansive operators with dissipative perturbations in cones},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {49--54},
     year = {1998},
     volume = {39},
     number = {1},
     mrnumber = {1622324},
     zbl = {0937.47053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1998_39_1_a4/}
}
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Chang, S. S.; Chen, Y. Q.; Cho, Y. J.; Lee, B. S. Fixed point theorems for nonexpansive operators with dissipative perturbations in cones. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 1, pp. 49-54. http://geodesic.mathdoc.fr/item/CMUC_1998_39_1_a4/