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New Necessary Conditions for a Fixed-Point of Maps in Non-Metric Spaces
Department of Mathematics and Computer Science, University of Arkansas at Pine Bluff, Pine Bluff, AR, USA
- 1 Department of Mathematics and Computer Science, University of Arkansas at Pine Bluff, Pine Bluff, AR, USA
Advances in Pure Mathematics·Volume 12 (2022)·Pages 561–564·Published 18 October 2022·DOI10.4236/apm.2022.1210043
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Abstract
Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function between the metric topological space and the non-metric topological space. Then we show that we can create a function h on the non-metric space Y , h : Y → Y and present necessary conditions for a fixed point of this map on this map on Y . Therefore, this gives an opportunity to take a best conclusion in some sense, when non-metrizable matter is under consideration.
KeywordsTopological SpaceCompact Metric SpaceFixed PointContraction MapNon-Metric Space
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