Topological vector space-valued cone metric spaces and fixed point theorems. (English) Zbl 1197.54063

Summary: We develop the theory of topological vector space valued cone metric spaces with nonnormal cones. We prove three general fixed point results in these spaces and deduce as corollaries several extensions of theorems about fixed points and common fixed points, known from the theory of (normed-valued) cone metric spaces. Examples are given to distinguish our results from the known ones.


54H25 Fixed-point and coincidence theorems (topological aspects)
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