Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Products of uniformly noncreasy spaces

Author: Andrzej Wisnicki
Journal: Proc. Amer. Math. Soc. 130 (2002), 3295-3299
MSC (2000): Primary 47H09, 47H10, 46B20
Published electronically: June 11, 2002
MathSciNet review: 1913009
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that finite products of uniformly noncreasy spaces with a strictly monotone norm have the fixed point property for nonexpansive mappings. It gives new and natural examples of superreflexive Banach spaces without normal structure but with the fixed point property.

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

  • 1. A. G. Aksoy and M. A. Khamsi, Nonstandard Methods in Fixed Point Theory, Springer-Verlag, New York/Berlin, 1990. MR 91i:47073
  • 2. J. M. Ayerbe Toledano, T. Domínguez Benavides and G. L ópez Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Birkhäuser Verlag, Basel, 1997. MR 99e:47070
  • 3. L. P. Belluce, W. A. Kirk and E. F. Steiner, Normal structure in Banach spaces, Pacific J. Math. 26 (1968), 433-440. MR 38:1501
  • 4. W. L. Bynum, A class of spaces lacking normal structure, Compositio Math. 25 (1972), 233-236. MR 47:7386
  • 5. T. Domínguez Benavides, Weak uniform normal structure in direct sum spaces, Studia Math. 103 (1992), 283-290. MR 94c:46024
  • 6. R. Espínola and W. A. Kirk, Fixed points and approximate fixed points in product spaces, Taiwanese J. Math. 5 (2001), 405-416. MR 2002b:54043
  • 7. K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics, Vol. 28, Cambridge Univ. Press, Cambridge, 1990. MR 92c:47070
  • 8. M. A. Japón Pineda, A new constant in Banach spaces and stability of the fixed point property, in Proc. of Workshop on Fixed Point Theory (Kazimierz Dolny, 1997), Ann. Univ. Mariae Curie-Sk\lodowska Sect. A 51 (1997), 135-141. MR 2000d:46015
  • 9. W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-6. MR 32:6436
  • 10. M. A. Khamsi, On normal structure, fixed-point property and contractions of type $\gamma $, Proc. Amer. Math. Soc. 106 (1989), 995-1001. MR 90d:46028
  • 11. T. Kuczumow, Fixed point theorems in product spaces, Proc. Amer. Math. Soc. 108 (1990), 727-729. MR 90e:47061
  • 12. T. Landes, Permanence properties of normal structure, Pacific J. Math. 110 (1984), 125-143. MR 86e:46014
  • 13. T. Landes, Normal structure and the sum-property, Pacific J. Math. 123 (1986), 127-147. MR 87h:46043
  • 14. K. Menger, Untersuchungen uber allgemeine metrik, Math. Ann. 100 (1928), 75-163.
  • 15. S. Prus, Banach spaces which are uniformly noncreasy, in Proc. 2nd World Congress of Nonlinear Analysts (Athens, 1996), ed. V. Lakshmikantham, Nonlinear Anal. 30 (1997), 2317-2324. MR 98m:46017
  • 16. B. Sims, Ultra-techniques in Banach Space Theory, Queen's Papers in Pure and Applied Math., Vol. 60, Queen's University, Kingston, Ont., 1982. MR 86h:46032
  • 17. B. Sims and M. A. Smyth, On some Banach space properties sufficient for weak normal structure and their permanence properties, Trans. Amer. Math. Soc. 351 (1999), 497-513. MR 99d:46020
  • 18. K.-K. Tan and H. K. Xu, On fixed point theorems of nonexpansive mappings in product spaces, Proc. Amer. Math. Soc. 113 (1991), 983-989. MR 92c:47074
  • 19. D. Tingley, The normal structure of James quasireflexive space, Bull. Austral. Math. Soc. 42 (1990) 95-100. MR 91h:46038

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47H09, 47H10, 46B20

Retrieve articles in all journals with MSC (2000): 47H09, 47H10, 46B20

Additional Information

Andrzej Wisnicki
Affiliation: Department of Mathematics, Maria Curie - Skłodowska University, 20-031 Lublin, Poland

Keywords: Nonexpansive mappings, fixed points
Received by editor(s): June 12, 2001
Published electronically: June 11, 2002
Additional Notes: This research was supported in part by KBN grant 2 PO3A 029 15.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society