Author(s)

Ivan Raykov

Department of Mathematics and Computer Science, University of Arkansas at Pine Bluff, Pine Bluff, AR, USA.

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.

Topological Space, Compact Metric Space, Fixed Point, Contraction Map, Non-Metric Space

Raykov, I. (2022) New Necessary Conditions for a Fixed-Point of Maps in Non-Metric Spaces. Advances in Pure Mathematics, 12, 561-564. doi: 10.4236/apm.2022.1210043.