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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On complex strict and uniform convexity


Author: J. Globevnik
Journal: Proc. Amer. Math. Soc. 47 (1975), 175-178
DOI: https://doi.org/10.1090/S0002-9939-1975-0355564-9
MathSciNet review: 0355564
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Abstract: Strict and uniform $ c$-convexity of complex normed spaces are introduced as a natural generalization of strict and uniform convexity. It is proved that the complex space $ {L_1}(S,\sigma ,\mu )$ is uniformly $ c$-convex. An application to analytic functions is given.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0355564-9
Keywords: Analytic functions, maximum modulus theorem, strictly and uniformly convex spaces
Article copyright: © Copyright 1975 American Mathematical Society

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