## 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)

### Citations:

Zbl 1118.54022; Zbl 0239.54032
Full Text: