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

Wenxi Pan; Jingshi Xu

doi:10.4995/agt.2006.1931

Authors

Wenxi Pan Jinan University
Jingshi Xu Hunan Normal University

DOI:

https://doi.org/10.4995/agt.2006.1931

Keywords:

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

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.

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Author Biographies

Wenxi Pan, Jinan University

Department of Mathematics

Jingshi Xu, Hunan Normal University

Department of Mathematics

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.