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Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

Shih-sen Chang, Yu-Qing Chen, Yeol Je Cho, Byung-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 ) .

Fixed point theorems for weakly sequentially closed maps

Donal O'Regan (2000)

Archivum Mathematicum

A number of fixed point theorems are presented for weakly contractive maps which have weakly sequentially closed graph. Our results automatically lead to new existence theorems for differential inclusions in Banach spaces relative to the weak topology.

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