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References
Z.Altschuler, The modulus of convexity of Lorentz and Orlicz sequence spaces. Notes in Banach spaces (H. E. Lacey ed.), 359–378, University of Texas 1980.
J.Diestel, Geometry of Banach spaces — selected topics. Berlin-Heidelberg-New York 1975.
J.Diestel, Sequences and series in Banach spaces. Berlin-Heidelberg-New York 1984.
T. Figiel, On the moduli of convexity and smoothness. Studia Math.56, 121–155 (1976).
K.Goebel and S.Reich, Uniform convexity, hyperbolic geometry and nonexpansive map pings. New York-Basel 1984.
O. Hanner, On the uniform convexity ofL p andl p . Ark. Mat.3, 239–244 (1956).
H. Hudzik, An estimation of the modulus of convexity in a class of Orlicz spaces. Math. Japon. (2)32, 227–237 (1987).
H. Hudzik, On some equivalent conditions in Musielak-Orlicz spaces. Comment. Math. Prace Mat.24, 57–64 (1984).
A. Kamińska, Flat Orlicz-Musielak sequence spaces. Bull. Acad. Polon. Sci. Math.30, 347–352 (1982).
M. A.Krasnoselskii and Ya. B.Rutickii, Convex functions and Orlicz spaces. Groningen 1961 (translation).
J. Lamperti, On the isometries of certain function spaces. Pacific J. Math.8, 459–466 (1958).
K. J. Lindberg, On subspaces of Orlicz sequence spaces. Studia Math.4, 119–146 (1973).
J.Lindenstrauss and L.Trafriri, Classical Banach spaces I and II. Berlin-Heidelberg-New York 1977 and 1979.
W. A. J.Luxemburg, Banach function spaces. Delft 1956.
R. P. Maleev andS. L. Troyanski, On the moduli of convexity and smoothness in Orlicz spaces. Studia Math.54, 131–141 (1975).
L. Maligranda, Indices and interpolation. Dissertationes Math.234, 1–54 (1985).
W. Matuszewska, On a generalization of regularly increasing functions. Studia Math.24, 271–279 (1964).
W. Matuszewska andW. Orlicz, On some classes of functions with regards to their orders of growth. Studia Math.26, 11–24 (1965).
W. Matuszewska andW. Orlicz, On certain properties of ϕ-functions. Bull. Acad. Polon. Sci. Math.8, 439–443 (1960).
J.Musielak, Orlicz spaces and modular spaces. LNM1034, Berlin-Heidelberg-New York 1983.
J. B. Simonenko, Interpolation and extrapolation of linear operators in Orlicz spaces (Russian). Mat. Sb.63, 536–553 (1964).
B. Turett, Rotundity of Orlicz spaces. Proc. Koninkl. Nederl. Akad. Wet. Amsterdam A (5)79, 462–468 (1979).
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Hudzik, H. Lower and upper estimations of the modulus of convexity in some Orlicz spaces. Arch. Math 57, 80–87 (1991). https://doi.org/10.1007/BF01200043
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DOI: https://doi.org/10.1007/BF01200043