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Assad-Kirk-type fixed point theorems for a pair of nonself mappings on cone metric spaces. (English) Zbl 1186.54035
Let \(E\) be a real Banach space. A subset \(P\) of \(E\) is a cone [L. G. Huang and X. Zhang, J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)] if 7mm
(i)
\(P\) is closed, nonempty and \(P\neq\{0\}\);
(ii)
\(a,b\in \mathbb R\), \(a,b\geq 0\) and \(x,y\in P\) imply \(ax+ by\in P\);
(iii)
\(P\cap (-P)= \{0\}\).
In this paper new Assad-Kirk type fixed point theorems [N. A. Assad and W. A. Kirk, Pac. J. Math. 43, 553–562 (1972; Zbl 0239.54032)] for a pair of non-self mappings defined on a closed subset of a metrically convex cone metric space are obtained.

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