S.S. Chang, Y.Q. Chen, Y.J. Cho, B.S. Lee
Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

Comment.Math.Univ.Carolinae 39,1 (1998) 49-54.

Abstract: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 $L^2(\Omega )$.

Keywords: nonexpansive mapping, accretive mapping, fixed point theorem, nonlinear integral equations
AMS Subject Classification: 45H10, 47H06, 47H09, 47H15