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On ε - Birkhoff Orthogonality And ε - Near Best Approximation
Sharma, MeeNu,Narang, T. D. 한국수학교육학회 2001 純粹 및 應用數學 Vol.8 No.2
In this paper, the notion of ε-Birkhoff orthogonality introduced by Dragomir [An. Univ. Timis¿oara Ser. S¿tiint¿. Mat. 29 (1991), no. 1, 51-58] in normed linear spaces has been extended to metric linear spaces and a decomposition theorem has been proved. Some results of Kainen, Kurkova and Vogt [J. Apgarox. Theory 105 (2000), no. 2, 252-262] proved on e-near best approximation in normed linear spaces have also been extended to metric linear spaces. It is shown that if (X, d) is a convex metric linear space which is pseudo strictly convex and M a boundedly compact closed subset of X such that for each ε $gt; 0 there exists a continuous e-near best approximation φ : X → M of X by M then M is a chebyshev set.