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On the sum of best simultaneously proximinal subspaces

Year 2014, Volume: 43 Issue: 4, 595 - 602, 01.08.2014

Abstract

Let X be a Banach space and G a subspace of X. A point g0 ∈ G
is said to be a best simultaneous approximation for a bounded set
A ⊆ X if d(A, G) = inf
g∈G
sup
a∈A
ka − gk = sup
a∈A
ka − g0k. In this paper we
prove that if F and G are two subspaces of a Banach space X such
that G is reflexive and F is simultaneously proximinal, then F + G is
simultaneously proximinal provided that F ∩ G is finite dimensional
and F + G is closed. Some other related results are also presented.

References

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Year 2014, Volume: 43 Issue: 4, 595 - 602, 01.08.2014

Abstract

References

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There are 1 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Mahmoud Rawashdeh

Sh. Al-sharif This is me

W.b. Domi This is me

Publication Date August 1, 2014
Published in Issue Year 2014 Volume: 43 Issue: 4

Cite

APA Rawashdeh, M., Al-sharif, S., & Domi, W. (2014). On the sum of best simultaneously proximinal subspaces. Hacettepe Journal of Mathematics and Statistics, 43(4), 595-602.
AMA Rawashdeh M, Al-sharif S, Domi W. On the sum of best simultaneously proximinal subspaces. Hacettepe Journal of Mathematics and Statistics. August 2014;43(4):595-602.
Chicago Rawashdeh, Mahmoud, Sh. Al-sharif, and W.b. Domi. “On the Sum of Best Simultaneously Proximinal Subspaces”. Hacettepe Journal of Mathematics and Statistics 43, no. 4 (August 2014): 595-602.
EndNote Rawashdeh M, Al-sharif S, Domi W (August 1, 2014) On the sum of best simultaneously proximinal subspaces. Hacettepe Journal of Mathematics and Statistics 43 4 595–602.
IEEE M. Rawashdeh, S. Al-sharif, and W. Domi, “On the sum of best simultaneously proximinal subspaces”, Hacettepe Journal of Mathematics and Statistics, vol. 43, no. 4, pp. 595–602, 2014.
ISNAD Rawashdeh, Mahmoud et al. “On the Sum of Best Simultaneously Proximinal Subspaces”. Hacettepe Journal of Mathematics and Statistics 43/4 (August 2014), 595-602.
JAMA Rawashdeh M, Al-sharif S, Domi W. On the sum of best simultaneously proximinal subspaces. Hacettepe Journal of Mathematics and Statistics. 2014;43:595–602.
MLA Rawashdeh, Mahmoud et al. “On the Sum of Best Simultaneously Proximinal Subspaces”. Hacettepe Journal of Mathematics and Statistics, vol. 43, no. 4, 2014, pp. 595-02.
Vancouver Rawashdeh M, Al-sharif S, Domi W. On the sum of best simultaneously proximinal subspaces. Hacettepe Journal of Mathematics and Statistics. 2014;43(4):595-602.