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arXiv · 1708.08883

Fixed point properties and Q-nonexpansive retractions in locally convex spaces

Sompong Dhompongsa·Poom Kumam·Ebrahim Soori
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Abstract

Suppose that Q is a family of seminorms on a locally convex space E which determines the topology of E. We study the existence of Q-nonexpansive retractions for families of Q-nonexpansive mappings and prove that a separated and sequentially complete locally convex space $E$ that has the weak fixed point property, has the weak fixed point property for commuting separable semitopological semigroups of Q-nonexpansive mappings. This proves the Bruck's problem [5] for locally convex spaces. Moreover, we prove the existence of Q-nonexpansive retractions for the right amenable Q-nonexpansive semigroups.

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Sompong Dhompongsa, Poom Kumam, Ebrahim Soori. 2017-08-29. Fixed point properties and Q-nonexpansive retractions in locally convex spaces. https://arxiv.org/abs/1708.08883

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