Continuous selection, collectively fixed points and system of coincidence theorems in product topological spaces. (English) Zbl 1117.54032

Ding, Xie Ping

Acta Math. Sin., Engl. Ser. 22, No. 6, 1629-1638 (2006).

Summary: Some new continuous selection theorems are proved in noncompact topological spaces. As applications, some new collectively fixed point theorems and coincidence theorems for two families of set-valued mappings defined on product spaces of noncompact topological spaces are obtained under very weak assumptions. These results generalize many known results in the recent literature.

MSC:

54C65	Selections in general topology
47H10	Fixed-point theorems
54H25	Fixed-point and coincidence theorems (topological aspects)

Keywords:

continuous selection; collectively fixed point; coincidence theorem for two families of set-valued mappings; \(FC\)-space

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