Criteria of strong nearest-cross points and strong best approximation pairs

Wenxi Pan, Jingshi Xu

Abstract

The concept of strong nearest-cross point (strong n.c. point) is introduced, which is the generalization of strong uniqueness of best approximation from a single point. The relation connecting to localization is discussed. Some criteria of strong n.c. points are given. The strong best approximation pairs are also studied.


Keywords

Strong nearest-cross point; Local strong nearest-cross point; Strong best approximation pair

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References

P. Beneker and J. Wiegerinck, Strongly exposed points in uniform algebras, Proc. Amer. Math. Soc. 127 (1999), 1567-1570. http://dx.doi.org/10.1090/S0002-9939-99-05274-0

D. Braess, Nonlinear Approximation Theory, Springer-Verlag, Berlin, Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-61609-9

D. F. Mah, Strong uniqueness in nonlinear approximation, J. Approx. Theory 41 (1984), 91-99. http://dx.doi.org/10.1016/0021-9045(84)90104-7

W. Pan, The distance between sets and the properties of best approximation pairs, J. of Math. (Chinese), 14 (1994), 491-497.

W. Pan, On the existence and uniqueness of proximity pairs and nearest-cross points, J. Math. Research and exposition (Chinese), 15 (1995), 237-243.

W. Pan, Characterization of nearest-cross points in the problem of distance of two convex sets, J. Jinan Univ. (Natural Science) (Chinese), 20(3) (1999), 1-7.

P. L. Papini, Approximation and strong approximation in normed spaces via tangent function, J. Approx. Theory 22 (1978), 111-118. http://dx.doi.org/10.1016/0021-9045(78)90060-6

A. A. Tolstonogov, Strongly exposed points of decomposable sets in spaces of Bochner integrable functions, Mathematical Notes 71 (2002), 267-275. http://dx.doi.org/10.1023/A:1013971517443

Q. Wang, W. Pan, New concept of normal separation of two sets and its properties, Acta Sci. Nat. Univ. Sunyatseni (Chinese), 39(6) (2000), 20-25.

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Universitat Politècnica de València

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