Abstract
We study the best coapproximation problem in the Banach space by using Birkhoff–James orthogonality techniques. Given a subspace of , we completely identify the elements x in for which best coapproximations to x out of exist. The methods developed in this article are computationally effective and it allows us to present an algorithmic approach to the concerned problem. We also identify the coproximinal subspaces and co-Chebyshev subspaces of .
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