New Generalization of f‐Best Simultaneous Approximation in Topological Vector Spaces

Mahmoud Rawashdeh and Sarah Khalil

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: Let K be a nonempty subset of a Hausdorff topological vector space X, and let f be a real‐valued continuous function on X. If for each x = (x1, x2, …, xn) ∈ Xn, there exists k0 ∈ K such that FK(x)=∑i=1nfxi-k0=inf ∑i=1nf(xi-k):k∈K, then K is called f‐simultaneously proximal and k0 is called f‐best simultaneous approximation for x in K. In this paper, we study the problem of f‐simultaneous approximation for a vector subspace K in X. Some other results regarding f‐simultaneous approximation in quotient space are presented.

Date: 2013
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https://doi.org/10.1155/2013/978738

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:978738

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