Electron. J. Diff. Equ., Vol. 2011 (2011), No. 147, pp. 1-5.

Krasnosel'skii fixed point theorem for dissipative operators

Tian Xiang

In this note, a sufficient condition guaranteing the existence of fixed points in a nonempty, closed convex K for T+S is given, where $T:K\subset E\to E$ is dissipative and $S:K\to E$ is condensing. This may indicate a new direction of the Krasnoselskii type fixed point theorem.

Submitted July 22, 2011. Published November 3, 2011.
Math Subject Classifications: 37C25, 47H09,47H10, 47H30.
Key Words: Dissipative operator; condensing operator; fixed point.

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Tian Xiang
Department of Mathematics, Tulane University
New Orleans, LA 70118, USA
email: txiang@tulane.edu

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