Authors: Janković, Slobodanka 
Golubović, Zorana
Radenović, Stojan
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Compatible and weakly compatible mappings in cone metric spaces
Journal: Mathematical and Computer Modelling
Volume: 52
Issue: 9-10
First page: 1728
Last page: 1738
Issue Date: 1-Nov-2010
Rank: M22
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2010.06.043
In this paper we extend and generalize common fixed point theorems for six self-maps of Singh and Jain [B. Singh, S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl. 301 (2005) 439-448] from Menger and metric spaces to cone metric spaces. We also extend the notions of compatible and weakly compatible mappings from the setting of Menger and metric spaces to the setting of cone metric spaces. We do not impose the normality property on the cone, but suppose only that the cone P, in the ordered Banach space E, has a nonempty interior. Examples are given to illustrate the results.
Keywords: Common fixed point | Compatible maps | Cone metric space | Normal and non-normal cones | Weakly compatible
Publisher: Elsevier

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