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Another proof of the Browder–Göhde–Kirk theorem via ordering argument

  • Jacek Jachymski (a1)
Abstract

Using the Zermelo Principle, we establish a common fixed point theorem for two progressive mappings on a partially ordered set. This result yields the Browder–Göhde–Kirk fixed point theorem for nonexpansive mappings.

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References
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[1]Bourbaki, N., ‘Sur le théorème de Zorn’, Arch. Math. 2 (19491950), 434437.
[2]Dunford, N. and Schwartz, J., Linear operators I: general theory (Wiley Interscience, New York, 1957).
[3]Fuchssteiner, B., ‘Iterations and fixpoints’, Pacific J. Math. 68 (1977), 7380.
[4]Goebel, K. and Kirk, W.A., Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics 28 (Cambridge University Press, Cambridge, 1990).
[5]Kirk, W.A., ‘A fixed point theorem for mappings which do not increase distance’, Amer. Math. Monthly 72 (1965), 10041006.
[6]Kirk, W.A., ‘Nonexpansive mappings in metric and Banach spaces’, Rend. Sem. Mat. Fis. Milano 51 (1981), 133144.
[7]Zermelo, E., ‘Neuer Beweis für die Möglichkeit einer Wohlordnung’, Math. Ann. 65 (1908), 107128.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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