A modulus for property (β) of Rolewicz
Ayerbe, J. ; Domínguez Benavides, T. ; Cutillas, S.
Colloquium Mathematicae, Tome 72 (1997), p. 183-191 / Harvested from The Polish Digital Mathematics Library

We define a modulus for the property (β) of Rolewicz and study some useful properties in fixed point theory for nonexpansive mappings. Moreover, we calculate this modulus in lp spaces for the main measures of noncompactness.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:210484
@article{bwmeta1.element.bwnjournal-article-cmv73i2p183bwm,
     author = {J. Ayerbe and T. Dom\'\i nguez Benavides and S. Cutillas},
     title = {A modulus for property ($\beta$) of Rolewicz},
     journal = {Colloquium Mathematicae},
     volume = {72},
     year = {1997},
     pages = {183-191},
     zbl = {0899.46008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv73i2p183bwm}
}
Ayerbe, J.; Domínguez Benavides, T.; Cutillas, S. A modulus for property (β) of Rolewicz. Colloquium Mathematicae, Tome 72 (1997) pp. 183-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv73i2p183bwm/

[000] [AKPRS] R. R. Akhmerov, M. I. Kamenskiĭ, A. S. Potapov, A. E. Rodkina and B. N. Sadovskiĭ, Measures of Noncompactness and Condensing Operators, Birkhäuser, 1992.

[001] [ADF] J. M. Ayerbe, T. Domínguez Benavides and S. Francisco Cutillas, Some noncompact convexity moduli for the property (β) of Rolewicz, Comm. Appl. Nonlinear Anal. 1 (1994), 87-98. | Zbl 0861.46006

[002] [B1] J. Banaś, On modulus of noncompact convexity and its properties, Canad. Math. Bull. 30 (1987), 186-192. | Zbl 0585.46011

[003] [B2] J. Banaś, Compactness conditions in the geometric theory of Banach spaces, Nonlinear Anal. 16 (1991), 669-682. | Zbl 0724.46019

[004] [B] B. Beauzamy, Introduction to Banach Spaces and Their Geometry, North-Holland, 1986. | Zbl 0491.46014

[005] [By] W. L. Bynum, A class of spaces lacking normal structure, Compositio Math. 25 (1972), 233-236. | Zbl 0244.46012

[006] [DL] T. Domínguez Benavides and G. López Acedo, Lower bounds for normal structure coefficients, Proc. Roy. Soc. Edinburgh Sect. A 121 (1992), 245-252. | Zbl 0787.46010

[007] [GK] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990. | Zbl 0708.47031

[008] [GS] K. Goebel and T. Sękowski, The modulus of noncompact convexity, Ann. Univ. Mariae Curie-Skłodowska Sect. A 38 (1984), 41-48 . | Zbl 0607.46011

[009] [GGM] I. C. Gohberg, L. S. Goldenstein and A. S. Markus, Investigation of some properties of bounded linear operators in connection with their q-norms, Uchen. Zap. Kishinev. Un-ta 29 (1975), 29-36 (in Russian).

[010] [H] R. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 4 (1980), 743-749. | Zbl 0505.46011

[011] [K] K. Kuratowski, Sur les espaces complets, Fund. Math. 15 (1930), 301-309. | Zbl 56.1124.04

[012] [Ku] D. N. Kutzarova, k-(β) and k-nearly uniform convex Banach spaces, J. Math. Anal. Appl. 162 (1991), 322-338.

[013] [KMP] D. N. Kutzarova, E. Maluta and S. Prus, Property (β) implies normal structure of the dual space, Rend. Circ. Mat. Palermo 41 (1992), 353-368. | Zbl 0785.46013

[014] [KP] D. N. Kutzarova and P. L. Papini, On a characterization of property (β) and LUR, Boll. Un. Mat. Ital. A (7) 6 (1992), 209-214. | Zbl 0786.46019

[015] [M] R. H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Wiley Interscience, New York, 1976.

[016] [O] Z. Opial, Lecture Notes on Nonexpansive and Monotone Mappings in Banach Spaces, Center for Dynamical Systems, Brown University, 1967.

[017] [R1] S. Rolewicz, On drop property, Studia Math. 85 (1987), 27-35.

[018] [R2] S. Rolewicz, On Δ-uniform convexity and drop property, ibid. 87 (1987), 181-191.

[019] [S] B. N. Sadovskiĭ, On a fixed point principle, Funktsional. Anal. i Prilozhen. 4 (2) (1967), 74-76 (in Russian). | Zbl 0165.49102

[020] [WW] J. H. Wells and L. R. Williams, Embeddings and Extensions in Analysis, Springer, Berlin, 1975.