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Average distance constants for polygons in spaces with non-positive curvature

Published online by Cambridge University Press:  17 April 2009

Devendra K. Kulshestha ,
Tom W. Sag  and
Lu Yang
Devendra K. Kulshestha
Affiliation:
School of Mathematical Sciences The Flinders University of South Australia, Bedford Park SA 5042, Australia
Tom W. Sag
Affiliation:
School of Mathematical Sciences The Flinders University of South Australia, Bedford Park SA 5042, Australia
Lu Yang
Affiliation:
Institute of Mathematical Science Chengdu Branch, Academia Sinica Chengdu, China
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Abstract

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In this paper we show that the average distance constant of a general polygon which is a subset of an M-space with non-positive curvature can be expressed as the extreme value of either of two nonlinear programs and discuss the practical application of one of these nonlinear programs for the determination of the average distance constant for a polygon in general, and in particular for a planar triangle.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 2 , October 1990 , pp. 323 - 333
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Busemann, H. and Phadke, B.B., Spaces with Distinguished Geodesies (Marcel Dekker, New York and Basel, 1987).Google Scholar
[2]Cleary, J., Morris, S.A. and Yost, D., ‘Numerical geometry-numbers for shapes’, Amer. Math. Monthly 93 (1986), 260–275.CrossRefGoogle Scholar
[3]Freese, R., Murphy, G. and Andalafte, E., ‘Strict convexity in M-space’, J. Geometry 34 (1989), 42–49.CrossRefGoogle Scholar
[4]Gross, O., ‘The rendezvous value of a metric space’, Ann. of Math. Studies, Princeton 24 (1969), 49–53.Google Scholar
[5]Li, Liu, Lu, Yang and Jingzhong, Zhang, ‘Average distance constants of polygons in Euclidean space’, Scientifica Sinica (to appear).Google Scholar
[6]Lu, Yang and Jingzhong, Zhang, ‘Average distance constants of some compact convex spaces’, J. China Univ. Sci. Tech. 17 (1987), 17–23.Google Scholar
[7]Morris, S.A. and Nickolas, P., ‘On the average distance property of compact connected metric spaces’, Arch. Math. 40 (1983), 458–483.CrossRefGoogle Scholar
[8]Nickolas, P. and Yost, D., ‘The average distance property for subsets of Euclidean spaces’, Arch. Math. 50 (1988), 380–384.CrossRefGoogle Scholar
[9]Powell, M.J.D., ‘An efficient method for finding the minimum of a function of several variables without calculating derivatives’, Computer J. 7 (1964), 155–162.CrossRefGoogle Scholar
[10]Stadje, W., ‘A property of compact connected spaces’, Arch. Math. 36 (1981), 275–280.CrossRefGoogle Scholar
[11]Stantzen, J., ‘An average distance result in Euclidean n-space’, Bull. Austral. Math. Soc. 26 (1982), 321–330.CrossRefGoogle Scholar
[12]Van Tiel, J., Convex Analysis (John Wiley and Sons, New York, 1984).Google Scholar
[13]Yost, D., ‘Average distances in compact connected spaces’, Bull. Austral. Math. Soc. 26 (1982), 331–342.CrossRefGoogle Scholar
[14]Zhenbing, Zhen, ‘The average distance constants of skeletons of polygons and polyhedrons’, Math. Practice Theory 4 (1987), 30–35.Google Scholar