Necessary Conditions for a Fixed Point of Maps in Non-Metric Spaces

Abstract

The main purpose of the present work is to introduce necessary conditions for a map on a non-metric space, defined by using a map on a metric space, to have a fixed point.

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I. Raykov, "Necessary Conditions for a Fixed Point of Maps in Non-Metric Spaces," Advances in Pure Mathematics, Vol. 2 No. 6, 2012, pp. 371-372. doi: 10.4236/apm.2012.26055.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] A. V. Arhangel’skii and V. V. Fedorchuk, “The Basic Concepts and Constructions of General Topology,” In: A. V. Arkhangel’skii and L. S. Pontrjagin, Eds., General Topology I, Encyclopedia of the Mathematical Sciences, Springer, Berlin, 1990.
[2] J. Dugundji, “Topology,” Allyn and Bacon, Inc., Boston, 1966.
[3] S. W. Davis, “Topology,” McGraw-Hill, Boston, 2005.
[4] L. Gorniewicz, “Topological Fixed Point Theory of Multivalued Mappings,” Springer Verlag, Berlin, 2006.

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