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2010-11-23 Nonlinear Seminar

Marcin Wachowiak
A fixed point theorem for mappings satisfying the interior condition

In this talk, we will prove a fixed point theorem for condensing mappings satisfying a new Leray-Schauder type condition proposed by Antonio Jimenez-Melado and Claudio H. Morales, the so-called interior condition. We will also show some examples, proving that this condition is in general independent of the classical Leray-Schauder boundary condition. Finally, we will prove that for nonexpansive mappings of Hilbert spaces, the interior condition implies the Leray-Schauder condition.