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2014 | 68 | 1 |
Tytuł artykułu

A fixed point theoremfor nonexpansive compact self-mapping

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EN
Abstrakty
EN
A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject.
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68
Numer
1
Opis fizyczny
Daty
wydano
2014
online
2015-05-23
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autor
Bibliografia
  • Agarwal, R. P., Meehan, M., O’Regan, D., Fixed Point Theory and Applications, Cambridge University Press, Cambridge, 2001.
  • Beg, I., Abbas, M., Fixed points and best approximation in Menger convex metric spaces, Arch. Math. (Brno) 41 (2005), 389-397.
  • Beg, I., Shahzad, N., Iqbal, M., Fixed point theorems and best approximation in convex metric spaces, J. Approx. Theory 8 (1992), 97-105.
  • Dotson Jr., W. G., Fixed-point theorems for nonexpansive mappings on starshaped subset of Banach spaces, J. London Math. Soc. 2 (1972), 408-410.
  • Dotson Jr., W. G., On fixed points of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc. 38 (1973), 155-156.
  • Dugundji, J., Granas, A., Fixed Point Theory, PWN-Polish Sci. Publ., Warszawa, 1982.
  • Goebel, K., Kirk, W. A., Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990.
  • Guay, M. D., Singh, K.L., Whitfield, J. H. M., Fixed point theorems for nonexpansive mappings in convex metric spaces, Proc. Conference on nonlinear analysis (Ed. S.P. Singh and J.H. Bury), Marcel Dekker, New York, 1982, 179-189.
  • Habiniak, L., Fixed point theory and invariant approximations, J. Approx. Theory 56 (1989), 241-244.
  • Singh, S., Watson, B., Srivastava, P., Fixed Point Theory and Best Approximation: The KKM-map Principle, Kluwer Academic Publishers, Dordrecht, 1997.
  • Schauder, J., Der fixpunktsatz in funktionaraumen, Studia Math. 2 (1930), 171-180.
  • Takahashi, W., A convexity in metric space and nonexpansive mappings, I, Kodai Math. Sem. Rep. 22 (1970), 142-149.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_43
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