Efficacy of cones on topological vector spaces and application to common fixed points of multifunctions.(English)Zbl 1198.54087

Summary: Let $$(E, \tau )$$ be a topological vector space and $$P$$ a cone in $$E$$. We shall define a topology $$\tau_P$$ on $$E$$ so that $$(E, \tau_P)$$ is a normable topological vector space and $$P$$ is a normal cone with normal constant $$M = 1$$. Then by using the norm, we shall give some results about common fixed points of two multifunctions on cone metric spaces.

MSC:

 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems
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References:

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