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The modulus of near smoothness of the lp product of a sequence of Banach spaces

Published online by Cambridge University Press:  18 May 2009

Leszek Olszowy
Leszek Olszowy
Affiliation:
Department of Mathematics, Technical University of Rzeszów, W. Pola 2, 35-959 Rzeszów, Poland E-Mail: lolszowy@prz.rzeszow.pl
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In the classical geometry of Banach spaces the notions of smoothness, uniform smoothness, strict and uniform convexity introduced by Day [1] and Clarkson [2] play a very important role and are used in many branches of functional analysis ([3,4,5], for example). In recent years a lot of papers have appeared containing interesting generalizations of these notions in terms of a measure of noncompactness. These new concepts investigated in this paper as near uniform smoothness, local near uniform smoothness and modulus of near smoothness have been introduced by Stachura and Sekowski [6] and Banaś [7] (see also [8,9]).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 2 , May 1997 , pp. 153 - 165
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

1.Day, M. M., Uniformly convexity in factor and conjugate spaces, Ann. of Math. (2) 45 (1944), 375–385.CrossRefGoogle Scholar
2.Clarkson, J. A., Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396–414.CrossRefGoogle Scholar
3.Day, M. M., Normed Linear Spaces (Springer, 1973).CrossRefGoogle Scholar
4.Kirk, W. A., Fixed point theory for nonexpansive mappings II, Contemp. Math. 18 (1983), 121–140.CrossRefGoogle Scholar
5.Köthe, G., Topological Vector Spaces I (Springer, 1969).Google Scholar
6.Sekowski, T. and Stachura, A., Noncompact smoothness and noncompact convexity, Atti. Sem. Mat. Fis. Univ. Modena 36 (1988), 329–338.Google Scholar
7.Banaś, J., Compactness conditions in the geometric theory of Banach spaces, Nonlinear Anal. 16 (1991), 669–682.CrossRefGoogle Scholar
8.Banaś, J. and Fraczek, K., Locally nearly uniformly smooth Banach spaces, Collect. Math. 44 (1993), 13–22.Google Scholar
9.Banaś, J. and Fraczek, K., Conditions involving compactness in geometry of Banach spaces, Nonlinear Anal. 20 (1993), 1217–1230.CrossRefGoogle Scholar
10.Banaś, J. and Goebel, K., Measure of noncompactness in Banach spaces, Lecture Notes in Pure and Appl. Math. 60 (Marcel Dekker, 1980).Google Scholar
11.Partington, J. R., On nearly uniformly convex Banach spaces, Math. Proc. Cambridge Philos. Soc. 93 (1983), 127–129.CrossRefGoogle Scholar
12.Leonard, I. E., Banach sequence spaces, J. Math. Anal. Appl. 54 (1976), 245–265.CrossRefGoogle Scholar