JOURNAL BROWSE
Search
Advanced SearchSearch Tips
CHARACTERIZATIONS OF GEOMETRICAL PROPERTIES OF BANACH SPACES USING ψ-DIRECT SUMS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
CHARACTERIZATIONS OF GEOMETRICAL PROPERTIES OF BANACH SPACES USING ψ-DIRECT SUMS
Zhang, Zhihua; Shu, Lan; Zheng, Jun; Yang, Yuling;
  PDF(new window)
 Abstract
Let X be a Banach space and a continuous convex function on satisfying certain conditions. Let be the -direct sum of X. In this paper, we characterize the K strict convexity, K uniform convexity and uniform non--ness of Banach spaces using -direct sums.
 Keywords
absolute norm;K strict convexity;K uniform convexity;uniform non--ness;
 Language
English
 Cited by
 References
1.
B. Beauzamy, Introduction to Banach Spaces and Their Geometry, 2nd ed., North Holland, 1985.

2.
F. F. Bonsall and J. Duncan, Numerical Ranges. II, London Mathematical Society Lecture Notes Series, No. 10. Cambridge University Press, New York-London, 1973.

3.
S. Dhompongsa, A. Kaewcharoen, and A. Kaewkhao, Fixed point property of direct sums, Nonlinear Anal. 63 (2005), 2177-2188. crossref(new window)

4.
S. Dhompongsa, A. Kaewkhao, and S. Saejung, Uniform smoothness and U-convexity of ${\psi}$-direct sums, J. Nonlinear Convex Anal. 6 (2005), no. 2, 327-338.

5.
P. N. Dowling and B. Turett, Complex strict convexity of absolute norms on Cn and direct sums of Banach spaces, J. Math. Anal. Appl. 323 (2006), no. 2, 930-937. crossref(new window)

6.
M. Kato, K.-S. Saito, and T. Tamura, On ${\psi}$-direct sums of Banach spaces and convexity, J. Aust. Math. Soc. 75 (2003), no. 3, 413-422. crossref(new window)

7.
M. Kato, K.-S. Saito, and T. Tamura, Uniform non-squareness of ${\psi}$-direct sums of Banach spaces $X{\bigoplus}_{\psi}Y$, Math. Inequal. Appl. 7 (2004), no. 3, 429-437.

8.
M. Kato, K.-S. Saito, and T. Tamura, Sharp triangle inequality and its reverse in Banach spaces, Math. Inequal. Appl. 10 (2007), no. 2, 451-460.

9.
M. Kato, K.-S. Saito, and T. Tamura, Uniform non- $l_{1}^{n}$-ness of ${\psi}$-direct sums of Banach spaces, J. Nonlinear Convex Anal. 11 (2010), no. 1, 13-33.

10.
R. E. Megginson, An Introduction to Banach Spaces Theory, Springer, 1998.

11.
K.-I. Mitani and K.-S. Saito, A note on geometrical properties of Banach spaces using ${\psi}$-direct sums, J. Math. Anal. Appl. 327 (2007), no. 2, 898-907. crossref(new window)

12.
K.-S. Saito and M. Kato, Uniform convexity of ${\psi}$-direct sums of Banach spaces, J. Math. Anal. Appl. 277 (2003), no. 1, 1-11. crossref(new window)

13.
K.-S. Saito, M. Kato, and Y. Takahashi, Absolute norms on $\mathbb{C}^{n}$, J. Math. Anal. Appl. 252 (2000), no. 2, 879-905. crossref(new window)

14.
I. Singer, On the set of best approximation of an element in a normed linear space, Rev. Math. Pures Appl. 5 (1960), 383-402.

15.
F. Sullivan, A generalization of uniformly rotund Banach spaces, Can. J. Math. 31 (1979), no. 3, 628-636. crossref(new window)

16.
Y. Takahashi, M. Kato, and K.-S. Saito, Strict convexity of absolute norms on $\mathbb{C}^{2}$ and direct sums of Banach spaces, J. Inequal. Appl. 7 (2002), no. 2, 179-186.

17.
X. T. Yu, E. B. Zang, and Z. Liu, On KUR Banach spaces, J. East China Normal Univ. Nature Science Edition. 1 (1981), 1-8.