Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Minimal displacement of points under holomorphic mappings and fixed point properties for unions of convex sets


Authors: Tadeusz Kuczumow, Simeon Reich and Adam Stachura
Journal: Trans. Amer. Math. Soc. 343 (1994), 575-586
MSC: Primary 47H10; Secondary 32K05, 47H09
MathSciNet review: 1242784
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let D be an open convex bounded subset of a complex Banach space $ (X,\left\Vert \cdot \right\Vert)$, and let C be the union of a finite number of closed convex sets lying strictly inside D. Using the Kuratowski measure of noncompactness with respect to the Kobayashi distance in D, we first show that if $ f:D \to D$ is a holomorphic mapping which leaves C invariant, and if the Lefschetz number $ \lambda ({f_{\vert C}}) \ne 0$, then $ \inf \{ \left\Vert {x - f(x)} \right\Vert:x \in C\} = 0$. We then deduce several new fixed point theorems for holomorphic and nonexpansive mappings.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47H10, 32K05, 47H09

Retrieve articles in all journals with MSC: 47H10, 32K05, 47H09


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1242784-0
PII: S 0002-9947(1994)1242784-0
Keywords: Fixed point, holomorphic mapping, Kobayashi distance, measure of noncompactness, minimal displacement, nonexpansive mapping
Article copyright: © Copyright 1994 American Mathematical Society