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Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

Shih-sen ChangYu-Qing ChenYeol Je ChoByung-Soo Lee — 1998

Commentationes Mathematicae Universitatis Carolinae

Let P be a cone in a Hilbert space H , A : P 2 P be an accretive mapping (equivalently, - A be a dissipative mapping) and T : P 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 ( Ω ) .

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