Renormings of c 0 and the minimal displacement problem

Łukasz Piasecki

Annales UMCS, Mathematica (2015)

  • Volume: 68, Issue: 2, page 85-91
  • ISSN: 2083-7402

Abstract

top
The aim of this paper is to show that for every Banach space (X, || · ||) containing asymptotically isometric copy of the space c0 there is a bounded, closed and convex set C ⊂ X with the Chebyshev radius r(C) = 1 such that for every k ≥ 1 there exists a k-contractive mapping T : C → C with [...] for any x ∊ C.

How to cite

top

Łukasz Piasecki. " Renormings of c 0 and the minimal displacement problem ." Annales UMCS, Mathematica 68.2 (2015): 85-91. <http://eudml.org/doc/270005>.

@article{ŁukaszPiasecki2015,
abstract = {The aim of this paper is to show that for every Banach space (X, || · ||) containing asymptotically isometric copy of the space c0 there is a bounded, closed and convex set C ⊂ X with the Chebyshev radius r(C) = 1 such that for every k ≥ 1 there exists a k-contractive mapping T : C → C with [...] for any x ∊ C.},
author = {Łukasz Piasecki},
journal = {Annales UMCS, Mathematica},
keywords = {Minimal displacement; asymptotically isometric copies of c0; lipschitzian mappings; k-contractive mappings; renormings; minimal displacement; asymptotically isometric copies of ; Lipschitzian map; renorming},
language = {eng},
number = {2},
pages = {85-91},
title = { Renormings of c 0 and the minimal displacement problem },
url = {http://eudml.org/doc/270005},
volume = {68},
year = {2015},
}

TY - JOUR
AU - Łukasz Piasecki
TI - Renormings of c 0 and the minimal displacement problem
JO - Annales UMCS, Mathematica
PY - 2015
VL - 68
IS - 2
SP - 85
EP - 91
AB - The aim of this paper is to show that for every Banach space (X, || · ||) containing asymptotically isometric copy of the space c0 there is a bounded, closed and convex set C ⊂ X with the Chebyshev radius r(C) = 1 such that for every k ≥ 1 there exists a k-contractive mapping T : C → C with [...] for any x ∊ C.
LA - eng
KW - Minimal displacement; asymptotically isometric copies of c0; lipschitzian mappings; k-contractive mappings; renormings; minimal displacement; asymptotically isometric copies of ; Lipschitzian map; renorming
UR - http://eudml.org/doc/270005
ER -

References

top
  1. [1] Bolibok, K., The minimal displacement problem in the space l∞, Cent. Eur. J. Math. 10 (2012), 2211-2214.[WoS] Zbl06137116
  2. [2] Bolibok, K., Constructions of lipschitzian mappings with non zero minimal displacement in spaces L1 (0, 1) and L2 (0, 1), Ann. Univ. Mariae Curie-Skłodowska Sec. A 50 (1996), 25-31. 
  3. [3] Dowling, P. N., Lennard C. J., Turett, B., Reflexivity and the fixed point property for nonexpansive maps, J. Math. Anal. Appl. 200 (1996), 653-662. Zbl0863.47038
  4. [4] Dowling, P. N., Lennard, C. J., Turett, B., Some fixed point results in l1 and c0, Nonlinear Anal. 39 (2000), 929-936. Zbl0954.47043
  5. [5] Dowling, P. N., Lennard C. J., Turett , B., Asymptotically isometric copies of c0 in Banach spaces, J. Math. Anal. Appl. 219 (1998), 377-391. Zbl0916.46007
  6. [6] Goebel, K., On the minimal displacement of points under lipschitzian mappings, Pacific J. Math. 45 (1973), 151-163. Zbl0265.47046
  7. [7] Goebel, K., Concise Course on Fixed Point Theorems, Yokohama Publishers, Yokohama, 2002. Zbl1066.47055
  8. [8] Goebel, K., Kirk, W. A., Topics in metric fixed point theory, Cambridge University Press, Cambridge, 1990. Zbl0708.47031
  9. [9] Goebel, K., Marino, G., Muglia, L., Volpe, R., The retraction constant and minimal displacement characteristic of some Banach spaces, Nonlinear Anal. 67 (2007), 735-744.[WoS] Zbl1126.46010
  10. [10] James, R. C., Uniformly non-square Banach spaces, Ann. of Math. 80 (1964), 542-550. Zbl0132.08902
  11. [11] Kirk, W. A., Sims, B. (Eds.), Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, Dordrecht, 2001. Zbl0970.54001
  12. [12] Lin, P. K., Sternfeld, Y., Convex sets with the Lipschitz fixed point property are compact, Proc. Amer. Math. Soc. 93 (1985), 633-639. Zbl0566.47039
  13. [13] Piasecki, Ł., Retracting a ball onto a sphere in some Banach spaces, Nonlinear Anal. 74 (2011), 396-399. [WoS] Zbl1208.47050

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.