On a generalized James constant

Journal of Mathematical Analysis and Applications

Volumn 285, Issue 2, 2003, Pages 419-435

  Dhompongsa, S ^a   Kaewkhao, A ^a   Tasena, S ^a  

^a CHIANG MAI UNIVERSITY   (Thailand)

Author keywords

James constant; Uniform normal structure; Uniformly nonsquare space

Indexed keywords

EID: 0141503446     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00408-6     Document Type: Article

References (27)

1. W.L. Bynum, Normal structure coefficients for Banach spaces, Pacific J. Math. 86 (1980) 427-436.
2. M.M. Day, Some characterizations of inner product spaces, Trans. Amer. Math. Soc. 62 (1947) 320-337.
3. S. Dhompongsa, P. Piraisangjun, S. Saejung, Generalized Jordan-von Neumann constants and uniform normal structure, Bull. Austral. Math. Soc. 67 (2003) 225-240.
4. T. Figiel, On the moduli of convexity and smoothness, Studia Math. 56 (1976) 121-155.
5. J. Gao, Normal hexagon and more general Banach spaces with uniform normal structure, J. Math. (Wuhan) 20 (2000) 241-248.
6. J. Gao, Normal structure and the arc length in Banach spaces, Taiwanese J. Math. 5 (2001) 353-366.
7. J. Gao, K.S. Lau, On the geometry of spheres in normed linear spaces, J. Austral. Math. Soc. Ser. A 48 (1990) 101-112.
8. J. Gao, K.S. Lau, On two classes of Banach spaces with uniform normal structure, Studia Math. 99 (1991) 41-56.
9. J. Garcia-Falset, The fixed point property in Banach spaces with NUS-property, J. Math. Anal. Appl. 215 (1997) 532-542.
10. J. Garcia-Falset, A. Jiménez-Melado, E. Llorens-Fuster, Stability of the fixed point property for nonexpansive mappings, in: W.A. Kirk, B. Sims (Eds.), Handbook of Metric Fixed Point Theory, Kluwer Academic, Dordrecht, 2001, pp. 201-238.
11. J. Garcia-Falset, B. Sims, Property (M) and the weak fixed point property, Proc. Amer. Math. Soc. 125 (1997) 2891-2896.
12. K. Goebel, Convexity of ball and fixed point theorems for mappings with nonexpansive square, Compositio Math. 22 (1970) 269-274.
13. K. Goebel, W.A. Kirk, Topics in Metric Fixed Point Theorem, Cambridge Univ. Press, Cambridge, 1990.
14. R.C. James, Uniformly non-square Banach spaces, Ann. of Math. 80 (1964) 542-550.
15. A. Jiménez-Melado, E. Llorens-Fuster, Opial modulus and stability of the fixed point property, Nonlinear Anal. 39 (2000) 341-349.
16. M. Kato, L. Maligranda, Y. Takahashi, On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces, Studia Math. 144 (2001) 275-295.
17. p spaces, Rev. Columbiana Mat. 28 (1994) 1-6.
18. W.A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965) 1004-1006.
19. K.S. Lau, Best approximation by closed sets in Banach spaces, J. Approx. Theory 23 (1978) 29-36.
20. P.K. Lin, Unconditional bases and fixed point of nonexpansive mappings, Pacific J. Math. 116 (1985) 69-76.
21. P.K. Lin, Stability of the fixed point property of Hilbert spaces, Proc. Amer. Math. Soc. 127 (1999) 3573-3581.
22. J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces II. Function Spaces, Springer-Verlag, Berlin, 1979.
23. R.E. Megginson, An Introduction to Banach Space Theory, in: Graduate Texts in Math., Vol. 183, Springer-Verlag, New York, 1998.
24. V.D. Milman, Geometric theory of Banach spaces. Theory of basic and minimal systems, Uspekhi Mat. Nauk 25 (1970) 113-174 (in Russian).
25. Z. Opial, Weak convergence of the sequences of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967) 591-597.
26. S. Prus, Multi-dimensional uniform convexity and uniform smoothness of Banach spaces, in: T. Dominguez Benavides (Ed.), Recent Advances on Metric Fixed Point Theory, Universidad de Sevilla, Sevilla, 1996, pp. 111-136.
27. B. Sims, A class of spaces with weak normal structure, Bull. Austral. Math. Soc. 49 (1994) 523-528.