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A note on k-uniformly convex spaces

Published online by Cambridge University Press:  24 October 2008

Jong Sook Bae  and
Sung Kyu Choi
Jong Sook Bae
Affiliation:
Department of Mathematics, Chungnam National UniversityDaejon 300-31, Korea
Sung Kyu Choi
Affiliation:
Department of Mathematics, Chungnam National UniversityDaejon 300-31, Korea
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Abstract

In this short note we prove that Istrǎƫescu's notion of k-uniform (k-locally uniform) convexity of a Banach space is actually equivalent to the notion of uniform (locally uniform) convexity. Thus theorem 2 in [3] and theorem 2·6·28 in [2] are trivially true.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 489 - 490
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Istrǎt̹escu, V. I.. Fixed Point Theory: An Introduction (D. Reidel, 1981).CrossRefGoogle Scholar
[2]Istrǎt̹escu, V. I.. Strict Convexity and Complex Strict Convexity: Theory and Applications. Lecture Notes in Math. (M. Dekker, 1983).Google Scholar
[3]Istrǎt̹escu, V. I. and Partington, J. R.. On nearly uniformly convex and k-uniformly convex spaces. Math. Proc. Cambridge Philos. Soc. 95 (1984), 325–327.CrossRefGoogle Scholar