References
J. Alonso andC. Benítez, The Joly's construction: a common property of some generalized orthogonalities. Bull. Soc. Math. Belg. Sér. B39, 277–285 (1987).
J. Alonso andC. Benítez, Some characteristic and non-characteristic properties of inner product spaces. J. Approx. Theory55, 318–325 (1988).
J. Banas, On moduli of smoothness of Banach spaces. Bull. Polish Acad. Sci. Math.34, 287–293 (1986).
J. A. Clarkson, Uniformly convex spaces. Trans. Amer. Math. Soc.40, 396–414 (1936).
M. M. Day, Uniform convexity in factor and conjugate spaces. Ann. of Math. (2)45, 375–385 (1944).
M. M. Day, Some characterizations of inner product spaces. Trans. Amer. Math. Soc.62, 320–337 (1947).
T. Figiel, On moduli of convexity and smoothness. Studia Math.56, 121–155 (1976).
C. Finet, Uniform convexity properties of norms on a super-reflexive Banach space. Israel J. Math.53, 81–92 (1986).
V. I. Gurarii, On the differentiability properties of the moduli of rotundity of Banach spaces. Mat. Issled.2, 141–148 (1967).
G.Köthe, Topological Vector Spaces I. Berlin-Heidelberg-New York 1983.
J. Lindenstrauss, On the modulus of smoothness and divergent series in Banach spaces. Michigan Math. J.10, 241–252 (1963).
R. McGuigan, Strongly extreme points in Banach spaces. Manuscripta Math.5, 113–122 (1971).
V. D. Milman, Infinite-dimensional geometry of the unit sphere in Banach space. Soviet Math. Dokl.8, 1440–1444 (1967).
G. Nordlander, The modulus of convexity in normed linear spaces. Ark. Mat.4, 15–17 (1960).
A. Ullán, Módulos de convexidad y lisura en Espacios Normados. Ph.D. Thesis, Univ. of Extremadura (Spain), 1990.
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Alonso, J., Ullán, A. Moduli in normed linear spaces and characterization of inner product spaces. Arch. Math 59, 487–495 (1992). https://doi.org/10.1007/BF01236044
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DOI: https://doi.org/10.1007/BF01236044