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


  • Wenxi Pan Jinan University
  • Jingshi Xu Hunan Normal University



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


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.


Download data is not yet available.

Author Biographies

Wenxi Pan, Jinan University

Department of Mathematics

Jingshi Xu, Hunan Normal University

Department of Mathematics


P. Beneker and J. Wiegerinck, Strongly exposed points in uniform algebras, Proc. Amer. Math. Soc. 127 (1999), 1567-1570.

D. Braess, Nonlinear Approximation Theory, Springer-Verlag, Berlin, Heidelberg, 1986.

D. F. Mah, Strong uniqueness in nonlinear approximation, J. Approx. Theory 41 (1984), 91-99.

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.

A. A. Tolstonogov, Strongly exposed points of decomposable sets in spaces of Bochner integrable functions, Mathematical Notes 71 (2002), 267-275.

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.


How to Cite

W. Pan and J. Xu, “Criteria of strong nearest-cross points and strong best approximation pairs”, Appl. Gen. Topol., vol. 7, no. 1, pp. 41–50, Apr. 2006.