Kodai Mathematical Journal

Modulus of convexity, characteristic of convexity and fixed point theorems

Hajime Ishihara and Wataru Takahashi

Full-text: Open access

Article information

Source
Kodai Math. J., Volume 10, Number 2 (1987), 197-208.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138037414

Digital Object Identifier
doi:10.2996/kmj/1138037414

Mathematical Reviews number (MathSciNet)
MR0897254

Zentralblatt MATH identifier
0654.47041

Subjects
Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Citation

Ishihara, Hajime; Takahashi, Wataru. Modulus of convexity, characteristic of convexity and fixed point theorems. Kodai Math. J. 10 (1987), no. 2, 197--208. doi:10.2996/kmj/1138037414. https://projecteuclid.org/euclid.kmj/1138037414


Export citation

References

  • [1] BAE, J. S., Reflexivity of a Banach space with a uniformly normal structure, Proc. Amer. Math. Soc. 90 (1984), 269-270.
  • [2] BROWDER, F. E., Nonexpansive nonlinear operators in Banach space, Proc. Nat Acad. Sci. U. S. A. 54(1965), 1041-1044.
  • [3] BYNUM, W. L., Normal structure coefficients for Banach spaces, Pacific J. Math 86 (1980), 427-436.
  • [4] CASINI, E. AND E. MALUTA, Fixed points of uniformly lipschitzian mappings i spaces with uniformly normal structure, Nonlinear Analysis 9 (1985), 103-108.
  • [5] DOWNING, D. J. AND W. O. RAY, Uniformly lipschitzian semigroup in Huber space, Canad. Math. Bull. 25 (1982), 210-214.
  • [6] DUNFORD, N. AND J. T. SCHWARTZ, Linear operators, Part 1., Interscience, Ne York (1958).
  • [7] GOEBEL, K., Convexity of balls and fixed-point theorems for mappings with non expansive square, Compositio Math. 22 Fasc. 3 (1970), 269-274.
  • [8] GOEBEL, K. AND W. A. KIRK, A fixed point theorem for transformations whos iterates have uniform Lipschitz constant, Studia Math. 47 (1973), 135-140.
  • [9] GOEBEL, K., W. A. KIRK AND R. L. THELE, Uniformly lipschitzian families o transformations in Banach space, Can. J. Math. 26 (1974), 1245-1256.
  • [10] GOHDE, D., Zum prinzip der kontraktiven abbildung, Math. Nachr. 30 (1965), 251-258
  • [11] GURARII, V. I., On the differential properties of the modulus of convexity in Banach space, Mat. Issled. 2 (1967), 141-148.
  • [12] ISHIHARA, H. AND W. TAKAHASHI, Fixed point theorems for uniformly lipschitzia semigroups in Hilbert spaces, to appear in J. Math. Anal. Appl. 126 (1987).
  • [13] KIRK, W. A., A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly 72 (1965), 1004-1006
  • [14] LIFSCHITZ, E. A., Fixed point theorems for operators in strongly convex spaces, Voronez Gos. Univ. Trudy Math. Fak. 16(1975), 23-28
  • [15] LIM, T. C, Characterizations of normal structure, Proc. Amer. Math. Soc. 4 (1974), 313-319.
  • [16] LIM, T. C, On asymptotic centers and fixed points of nonexpansive mappings, Can.J. Math. 32 (1980), 421-430
  • [17] MALUTA, E., Uniformly normal structure and related coefficients, Pacific J. Math 111 (1984), 357-369.
  • [18] TAKAHASHI, W., Fixed point theorems for families of nonexpansive mapping on unbounded sets, J. Math. Soc. Japan 36 (1984), 545-553.