Two Results on Jachymski–Schröder–Stein Contractions

Reich, Simeon; Zaslavski, Alexander J.

doi:10.4064/ba56-1-6

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Mean Nonexpansive Mappings1

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2012

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Cited by 12 publications

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“…Such mappings always have unique fixed points despite the fact that they may be discontinuous. Also, in addition to (9), if T is uniformly continuous, then convergence of the Picard iterates follows from a recent result of Reich and Zaslavski [48]. In looking to strengthen (8) to obtain a mapping with better properties, one might immediately think of the condition…”

Section: Mean Nonexpansive Mappingsmentioning

confidence: 99%

Remarks on the stability of the fixed point property for nonexpansive mappings

2012

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It is shown that in many instances the fixed point property for nonexpansive mappings actually implies the fixed point property for a strictly larger family of mappings. This paper is largely expository, but some of the observations are not readily available, and some appear here for the first time. Several related open questions in are discussed. The emphasis is on accessible problems, especially those that require little background. The problems themselves have been given little thought and may be trivial or difficult.

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Section: Mean Nonexpansive Mappingsmentioning

confidence: 99%