# Renormings of c 0 and the minimal displacement problem

Annales UMCS, Mathematica (2015)

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

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topŁukasz 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] Bolibok, K., The minimal displacement problem in the space l∞, Cent. Eur. J. Math. 10 (2012), 2211-2214.[WoS] Zbl06137116
- [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] 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] 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] 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] Goebel, K., On the minimal displacement of points under lipschitzian mappings, Pacific J. Math. 45 (1973), 151-163. Zbl0265.47046
- [7] Goebel, K., Concise Course on Fixed Point Theorems, Yokohama Publishers, Yokohama, 2002. Zbl1066.47055
- [8] Goebel, K., Kirk, W. A., Topics in metric fixed point theory, Cambridge University Press, Cambridge, 1990. Zbl0708.47031
- [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] James, R. C., Uniformly non-square Banach spaces, Ann. of Math. 80 (1964), 542-550. Zbl0132.08902
- [11] Kirk, W. A., Sims, B. (Eds.), Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, Dordrecht, 2001. Zbl0970.54001
- [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] Piasecki, Ł., Retracting a ball onto a sphere in some Banach spaces, Nonlinear Anal. 74 (2011), 396-399. [WoS] Zbl1208.47050