Abstract: The main purpose of this paper is to define the concept of $p$-normal structure and give some new fixed point theorems of nonexpansive maps in general topological space $(X,\tau)$ by introducing the notion of a $\tau$-symmetric function $p\colon X \times X \to \rit^+$. An application to symmetrizable topological spaces has been made.
Keywords: Hausdorff topological spaces, nonexpansive maps, normal structure, symmetrizable topological spaces.
Classification (MSC2000): 47H10
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