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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Some other related results are also presented.
📌 3 Key Takeaways
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Objective & Hypothesis:Let X be a Banach space and G a subspace of X.
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Key Findings & Data: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.
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Conclusion & Impact:Some other related results are also presented.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Approximation · simultaneously
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.
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Cite This Article
Rawashdeh, M., Al-sharif, S., Domi, W. (2014). On the sum of best simultaneously proximinal subspaces. Hacettepe Journal of Mathematics and Statistics, Volume: 43 Issue: 4. https://ajindex.com/articles/1403387