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Narang, T. D.

On best coapproximation in normed linear spaces. (English) Zbl 0757.41034

Rocky Mt. J. Math. 22, No. 1, 265-287 (1992).
This article is a summary of the research concerning best coapproximation. In this summary the author recommends results with regard to the existence and uniqueness of elements of best coapproximation by elements of linear subspaces, characterizations of elements of best coapproximation, characterizations of strict convexity in terms of best coapproximation, properties of the best coapproximation operator and best coapproximation on convex sets. All results mentioned here are given without proofs.
Reviewer: Zhang Ganglu (Dongying)

Cited in 5 Documents

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Keywords:

best coapproximation; strict convexity; convex sets
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\textit{T. D. Narang}, Rocky Mt. J. Math. 22, No. 1, 265--287 (1992; Zbl 0757.41034)
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References:

[1] M.W. Bartelt, Strongly unique best approximates to a function on a set, and a finite subset thereof , Pacific J. Math. 53 (1974), 1-9. · Zbl 0264.41014
[2] M.W. Bartelt and H.W. McLaughlin, Characterizations of strong unicity in approximation theory , J. Approx. Theory 9 (1973), 255-266. · Zbl 0273.41019
[3] H. Berens and U. Westphal, On the best coapproximation in a Hilbert space , in Quantitative approximation , Academic Press, 1980, 7-10. · Zbl 0484.41038
[4] G. Birkhoff, Orthogonality in linear metric spaces , Duke Math. J. 1 (1935), 169-172. · Zbl 0012.30604
[5] R.E. Bruck, Jr., Nonexpansive projections on subsets of Banach spaces , Pacific J. Math. 47 (1973), 341-355. · Zbl 0274.47030
[6] ——–, A characterization of Hilbert spaces , Proc. Amer. Math. Soc. 43 (1974), 173-175. · Zbl 0306.46027
[7] N. Dunford and J. Schwartz, Linear operators I, Interscience, New York, 1958. · Zbl 0084.10402
[8] S. Elumalai, A study of interpolation, approximation and strong approximation , Ph.D. Thesis, 1981.
[9] Carlo Franchetti, Chebyshev centres and hypercircles , Boll. Un. Mat. Ital. (4) 11 (1975), 565-573.
[10] C. Franchetti and M. Furi, Some characteristic properties of real Hilbert spaces , Rev. Roumaine Math. Pures Appl. 17 (1972), 1045-1048. · Zbl 0245.46024
[11] P. Gruber, Kontrahierende radialprojektionen in normierten räumen , Boll. Un. Mat. Ital. (4) 11 (1975), 10-21. · Zbl 0338.47029
[12] L. Hetzelt, On suns and cosuns in finite dimensional normed real vector spaces , Acta Math. Hung. 45 (1-2) (1985), 53-68. · Zbl 0592.41043
[13] R.C. James, Orthogonality and linear functionals in normed linear spaces , Trans. Amer. Math. Soc. 61 (1947), 265-292. JSTOR: · Zbl 0037.08001
[14] S. Muthukumar, A note on best and best simultaneous approximation , Indian J. Pure Appl. Math. 11 (1980), 715-719. · Zbl 0433.41011
[15] T.D. Narang, A study of farthest points . Nieuw Arch. Wisk. (4) 25 (1977), 54-79. · Zbl 0342.46009
[16] ——–, Convexity of Chebyshev sets , Nieuw Arch. Wisk. (4) 25 (1977), 377-402. · Zbl 0372.41021
[17] P.L. Papini, Some questions related to the concept of orthogonality in Banach spaces , proximity maps ; bases , Boll. Un. Mat. Ital. (4) 11 (1975), 44-63. · Zbl 0321.46014
[18] ——–, Approximation and strong approximation in normed spaces via tangent functionals , J. Approx. Theory 22 (1978), 111-118. · Zbl 0377.41024
[19] ——–, Sheltered points in normed spaces , Ann. Mat. Pura Appl. 67 (1978), 233-242. · Zbl 0393.41019
[20] P.L. Papini and Ivan Singer, Best approximation in normed linear spaces , Mh. Math. 88 (1979), 27-44. · Zbl 0421.41017
[21] Ivan Singer, Best approximation in normed linear spaces by elements of linear subspaces , Springer-Verlag, New York, 1970. · Zbl 0197.38601
[22] ——–, The theory of best approximation and functional analysis , CBMS- NSF Regional Conf. Ser. in Appl. Math. 13 (1974). · Zbl 0291.41020
[23] ——–, Some classes of nonlinear operators generalizing the metric projections onto Chebyshev subspaces , Proc. Fifth Internat. Summer school, Theory of Nonlinear Operators (Berlin 1977), Abh. Akad. Wiss. DDR, Abt. Math.-Naturwiss-Technik 6 N. (1978), 245-257. · Zbl 0431.47041
[24] Ryszard Smarzewski, Strong co-approximation in Banach spaces , J. Approx. Theory 55 (1988), 296-303. · Zbl 0675.41049
[25] U. Westphal, Cosuns in \(1^p(n), 1\leq p<\infty\) , J. Approx. Theory 54 (1988), 287-305. · Zbl 0658.41012
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