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1997 | 73 | 2 | 183-191
Tytuł artykułu

A modulus for property (β) of Rolewicz

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $l^p$ spaces for the main measures of noncompactness.
Rocznik
Tom
73
Numer
2
Strony
183-191
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-05-30
Twórcy
autor
  • Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain
  • Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain
  • Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain
Bibliografia
  • [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.
  • [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.
  • [B1] J. Banaś, On modulus of noncompact convexity and its properties, Canad. Math. Bull. 30 (1987), 186-192.
  • [B2] J. Banaś, Compactness conditions in the geometric theory of Banach spaces, Nonlinear Anal. 16 (1991), 669-682.
  • [B] B. Beauzamy, Introduction to Banach Spaces and Their Geometry, North-Holland, 1986.
  • [By] W. L. Bynum, A class of spaces lacking normal structure, Compositio Math. 25 (1972), 233-236.
  • [DL] T. Domínguez Benavides and G. López Acedo, Lower bounds for normal structure coefficients, Proc. Roy. Soc. Edinburgh Sect. A 121 (1992), 245-252.
  • [GK] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990.
  • [GS] K. Goebel and T. Sękowski, The modulus of noncompact convexity, Ann. Univ. Mariae Curie-Skłodowska Sect. A 38 (1984), 41-48 .
  • [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).
  • [H] R. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 4 (1980), 743-749.
  • [K] K. Kuratowski, Sur les espaces complets, Fund. Math. 15 (1930), 301-309.
  • [Ku] D. N. Kutzarova, k-(β) and k-nearly uniform convex Banach spaces, J. Math. Anal. Appl. 162 (1991), 322-338.
  • [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.
  • [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.
  • [M] R. H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Wiley Interscience, New York, 1976.
  • [O] Z. Opial, Lecture Notes on Nonexpansive and Monotone Mappings in Banach Spaces, Center for Dynamical Systems, Brown University, 1967.
  • [R1] S. Rolewicz, On drop property, Studia Math. 85 (1987), 27-35.
  • [R2] S. Rolewicz, On Δ-uniform convexity and drop property, ibid. 87 (1987), 181-191.
  • [S] B. N. Sadovskiĭ, On a fixed point principle, Funktsional. Anal. i Prilozhen. 4 (2) (1967), 74-76 (in Russian).
  • [WW] J. H. Wells and L. R. Williams, Embeddings and Extensions in Analysis, Springer, Berlin, 1975.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv73i2p183bwm
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