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

Rezapour, Shahram; Khandani, Hassan; Vaezpour, Seyyed M.

Rend. Circ. Mat. Palermo (2) 59, No. 2, 185-197 (2010).

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

Keywords:

common fixed point; multifunction; non-normal cone; topological vector space

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