References
J.Alonso and A.Ullán, Weak moduli of convexity. In: Proceedings of the II Congreso Análisis Funcional, Jarandilla, Spain, (1990), Extracta Math., 5–12.
D. Amir, Chebyshev centers and uniform convexity. Pacific J. Math.77, 1–6 (1978).
D. Amir andF. Deutsch, Approximation by certain subspaces in the Banach space of continuous vector-valued functions. J. Approx. Theory27, 254–270 (1979).
D. Amir andZ. Ziegler, Relative Chebyshev centers in normed linear spaces I. J. Approx. Theory29, 235–252 (1980).
D. Amir, J. Mach andK. Saatkamp, Existence of Chebyshev centers, bestn-nets and best compact approximants. Trans. Amer. Math. Soc.271, 513–524 (1982).
R. P. Boas, Some uniformly convex spaces. Bull. Amer. Math. Soc.46, 304–311 (1940).
J. A. Clarkson, Uniformly convex spaces. Trans. Amer. Math. Soc.40, 396–414 (1936).
J. Daněs, On local and global moduli of convexity. Comment. Math. Univ. Caroiin.17, 413–420 (1976).
M. M.Day, Normed linear spaces, 3rd Edition. Berlin-Heidelberg-New York 1973.
M. M. Day, Some more uniformly convex spaces. Bull. Amer. Math. Soc.47, 504–507 (1941).
M. M. Day, Uniform convexity III. Bull. Amer. Math. Soc.49, 745–750 (1943).
M. M. Day, Uniform convexity in factor and conjugate spaces. Ann. of Math.45, 375–385 (1944).
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).
H.Fakhoury, Directions d'uniform convexité dans un space normé. Séminaire Choquet, 14 année. Paris 1974.
G. Emmanuele andA. Villani, Lifting of rotundity properties fromE toL p(μ, E). Rocky Mountain J. Math.17, 617–627 (1987).
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.
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).
D. P. Giesy, On a convexity condition in normed linear spaces. Trans. Amer. Math. Soc.125, 114–146 (1966).
K.Goebel and W. A.Kirk, Topics in metric fixed point theory. Cambridge 1990.
A. Kamińska andB. Turett, Rotundity in Köthe spaces of vector-valued functions. Canad. J. Math.41, 659–675 (1989).
D. Kutzarova andT. Landes, Nearly uniform convexity of infinite direct sums. Indiana Math. J.41, 915–926 (1992).
J.Lindenstrauss and L.Tzafriri, Classical Banach spaces II. Berlin-Heidelberg-New York 1979.
E. J. McShane, Linear functional on certain Banach spaces. Proc. Amer. Math. Soc.1, 402–408 (1950).
R. R. Phelps, Uniqueness of Hahn-Banach extensions and unique best approximation. Trans. Amer. Math. Soc.95, 238–255 (1960).
M. A. Smith, Rotundity and extremity in ℓp(X i) andL r(μ, X). Contemp. Math.52, 143–162 (1986).
M. A. Smith andB. Turret, Rotundity in Lebesgue-Bochner function spaces. Trans. Amer. Math. Soc.257, 105–118 (1980).
A.Ullán, Módulos de convexidad y lisura en espacios normados. Publ. Dep. Matemáticas Univ. Extremadura27, Thesis, 1991.
A. C.Zaanen, Integration, 2nd Edition. Amsterdam 1967.
V. Zizler, On some rotundity and smoothness properties in Banach spaces. Dissertationes Math.87, 1–37 (1971).
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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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DOI: https://doi.org/10.1007/BF01196581