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Relative rotundity inL p(X)

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References

  1. J.Alonso and A.Ullán, Weak moduli of convexity. In: Proceedings of the II Congreso Análisis Funcional, Jarandilla, Spain, (1990), Extracta Math., 5–12.

  2. D. Amir, Chebyshev centers and uniform convexity. Pacific J. Math.77, 1–6 (1978).

    Google Scholar 

  3. D. Amir andF. Deutsch, Approximation by certain subspaces in the Banach space of continuous vector-valued functions. J. Approx. Theory27, 254–270 (1979).

    Google Scholar 

  4. D. Amir andZ. Ziegler, Relative Chebyshev centers in normed linear spaces I. J. Approx. Theory29, 235–252 (1980).

    Google Scholar 

  5. D. Amir, J. Mach andK. Saatkamp, Existence of Chebyshev centers, bestn-nets and best compact approximants. Trans. Amer. Math. Soc.271, 513–524 (1982).

    Google Scholar 

  6. R. P. Boas, Some uniformly convex spaces. Bull. Amer. Math. Soc.46, 304–311 (1940).

    Google Scholar 

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

    Google Scholar 

  8. J. Daněs, On local and global moduli of convexity. Comment. Math. Univ. Caroiin.17, 413–420 (1976).

    Google Scholar 

  9. M. M.Day, Normed linear spaces, 3rd Edition. Berlin-Heidelberg-New York 1973.

  10. M. M. Day, Some more uniformly convex spaces. Bull. Amer. Math. Soc.47, 504–507 (1941).

    Google Scholar 

  11. M. M. Day, Uniform convexity III. Bull. Amer. Math. Soc.49, 745–750 (1943).

    Google Scholar 

  12. M. M. Day, Uniform convexity in factor and conjugate spaces. Ann. of Math.45, 375–385 (1944).

    Google Scholar 

  13. M. M. Day, R. C. James andS. Swaminathan, Normed linear spaces that are uniformly convex in every direction. Canad. J. Math.26, 1051–1059 (1971).

    Google Scholar 

  14. H.Fakhoury, Directions d'uniform convexité dans un space normé. Séminaire Choquet, 14 année. Paris 1974.

  15. G. Emmanuele andA. Villani, Lifting of rotundity properties fromE toL p(μ, E). Rocky Mountain J. Math.17, 617–627 (1987).

    Google Scholar 

  16. A. L.Garkavi, On the Čebyšev center of a set in a normed space. In: Investigations of contemporary problems in the constructive theory of functions. 328–331. Moscow 1961.

  17. A. L. Garkavi, The best possible net and the best possible cross-section of a set in a normed space. Izv. Akad. Nauk SSSR Ser. Mat.26, 87–106 (1962); Amer. Math. Soc. Transl. Ser. 239, 111–132 (1964).

    Google Scholar 

  18. D. P. Giesy, On a convexity condition in normed linear spaces. Trans. Amer. Math. Soc.125, 114–146 (1966).

    Google Scholar 

  19. K.Goebel and W. A.Kirk, Topics in metric fixed point theory. Cambridge 1990.

  20. A. Kamińska andB. Turett, Rotundity in Köthe spaces of vector-valued functions. Canad. J. Math.41, 659–675 (1989).

    Google Scholar 

  21. D. Kutzarova andT. Landes, Nearly uniform convexity of infinite direct sums. Indiana Math. J.41, 915–926 (1992).

    Google Scholar 

  22. J.Lindenstrauss and L.Tzafriri, Classical Banach spaces II. Berlin-Heidelberg-New York 1979.

  23. E. J. McShane, Linear functional on certain Banach spaces. Proc. Amer. Math. Soc.1, 402–408 (1950).

    Google Scholar 

  24. R. R. Phelps, Uniqueness of Hahn-Banach extensions and unique best approximation. Trans. Amer. Math. Soc.95, 238–255 (1960).

    Google Scholar 

  25. M. A. Smith, Rotundity and extremity in ℓp(X i) andL r(μ, X). Contemp. Math.52, 143–162 (1986).

    Google Scholar 

  26. M. A. Smith andB. Turret, Rotundity in Lebesgue-Bochner function spaces. Trans. Amer. Math. Soc.257, 105–118 (1980).

    Google Scholar 

  27. A.Ullán, Módulos de convexidad y lisura en espacios normados. Publ. Dep. Matemáticas Univ. Extremadura27, Thesis, 1991.

  28. A. C.Zaanen, Integration, 2nd Edition. Amsterdam 1967.

  29. V. Zizler, On some rotundity and smoothness properties in Banach spaces. Dissertationes Math.87, 1–37 (1971).

    Google Scholar 

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Fernández, M., Palacios, I. Relative rotundity inL p(X). Arch. Math 65, 61–68 (1995). https://doi.org/10.1007/BF01196581

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