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Some examples concerning rotundity in Banach spaces

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  1. Anderson, K. W.: Midpoint local uniform convexity, and other geometric properties of Banach spaces. Dissertation, University of Illinois 1960

  2. Brodskii, M. S., Mil'man, D. P.: On the center of a convex set. Dokl. Akad. Nauk SSSR (N. S.)59, 837–840 (1948)

    Google Scholar 

  3. Clarkson, J.A.: Uniformly convex spaces. Trans. Amer. Math. Soc.40, 396–414 (1936)

    Google Scholar 

  4. Cudia, D. F.: Rotundity. In: Proc. Symp. Pure Math., pp. 73–97. Providence, R. I.: Amer. Math. Soc. 1963

    Google Scholar 

  5. Day, M. M.: Strict convexity and smoothness of normed spaces. Trans. Amer. Math. Soc.78, 516–528 (1955)

    Google Scholar 

  6. Day, M. M., James, R. C., Swaminathan, S.: Normed linear spaces that are uniformly convex in every direction. Canad. J. Math.23, 1051–1059 (1971)

    Google Scholar 

  7. Fan, K., Glicksberg, I.: Some geometric properties of the sphere in a normed linear space. Duke Math. J.25, 553–568 (1958)

    Google Scholar 

  8. Garkavi, A. L.: The best possible net and best possible cross section of a set in a normed space. Izv. Akad. Nauk SSSR Ser. Mat.26, 87–106 (1962)

    Google Scholar 

  9. Lovaglia, A. R.: Locally uniformly convex Banach spaces. Trans. Amer. Math. Soc.78, 225–238 (1955)

    Google Scholar 

  10. Rainwater, J.: Local uniform convexity of Day's norm onc 0(Г). Proc. Amer. Math. Soc.22, 335–339 (1969)

    Google Scholar 

  11. Smith, M. A.: Banach spaces that are uniformly rotund in weakly compact sets of directions. Canad. J. Math.29, 963–970 (1977)

    Google Scholar 

  12. Šmul'yan, V. L.: Sur la dérivabilité de la norme dans l'espace de Banach. C. R. (Doklady) Akad. Sci. URSS27, 643–648 (1940)

    Google Scholar 

  13. Zizler, V.: On some rotundity and smoothness properties of Banach spaces. Dissertationes Math. (Rozprawy Mat.) No. 87. Warsaw: Inst. Mat. Polsk. Akad. Nauk. 1971

    Google Scholar 

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Some of the examples in this paper appear in the author's Ph.D. thesis written at the University of Illinois under the supervision of Professor M. M. Day

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Smith, M.A. Some examples concerning rotundity in Banach spaces. Math. Ann. 233, 155–161 (1978).

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