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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.8 No.2

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ON <TEX>$\varepsilon$</TEX>-BIRKHOFF ORTHOGONALITY AND <TEX>$\varepsilon$</TEX>-NEAR BEST APPROXIMATION

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2001, v.8 no.2, pp.153-162
Sharma, Meenu (Department of Mathematics, Guru Nanak Dev University)
Narang, T.D. (Department of Mathematics, Guru Nanak Dev University)
Sharma, Meenu, & Narang, T.D.. (2001). ON <TEX>$\varepsilon$</TEX>-BIRKHOFF ORTHOGONALITY AND <TEX>$\varepsilon$</TEX>-NEAR BEST APPROXIMATION. 한국수학교육학회지시리즈B:순수및응용수학, 8(2), 153-162.

Abstract

In this Paper, the notion of <TEX>$\varepsilon$</TEX>-Birkhoff orthogonality introduced by Dragomir [An. Univ. Timisoara Ser. Stiint. 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. Approx. 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 <TEX>$\varepsilon$</TEX>>0 there exists a continuous <TEX>$\varepsilon$</TEX>-near best approximation <TEX>$\phi$</TEX> : X → M of X by M then M is a chebyshev set .

keywords
Proximinal set, Chebyshev set, approximatively compact set, pseudo/strict convexity, <tex> $\varepsilon$</tex>-Birkhoff orthogonality, <tex> $\varepsilon$</tex>-near best approximation

한국수학교육학회지시리즈B:순수및응용수학

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