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Li, Zhilong; Jiang, Shujun

On fixed point theory of monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces. (English) Zbl 1273.54064

Abstr. Appl. Anal. 2013, Article ID 349305, 6 p. (2013).
Summary: We presented some maximal and minimal fixed point theorems of set-valued monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces. In addition, we proved not only the existence of maximal and minimal fixed points but also the existence of the largest and the least fixed points of single-valued increasing mappings. It is worth mentioning that the results on single-valued mappings in this paper are still new even in the case of metric spaces and hence they indeed improve the recent results.

Cited in 1 Document

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
54C60 Set-valued maps in general topology
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\textit{Z. Li} and \textit{S. Jiang}, Abstr. Appl. Anal. 2013, Article ID 349305, 6 p. (2013; Zbl 1273.54064)
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