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2014-10-07 Nonlinear Seminar

Marcin Borkowski
Fixed point theorems with a boundary condition

In 1998, Espínola and López proved a certain fixed point theorem for a mapping transforming an admissible subset $$ A $$ of a hyperconvex metric space into the whole space, assuming that this mapping sends the boundary of $$ A $$ into $$ A $$. We will show how to simplify their proof considerably, at the same time relaxing its assumptions. In particular, this will enable proving a new fixed point theorem, generalizing a classical result of Baillon from 1988.

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