Existence of strong coupled fixed points for cyclic coupled Ciric-type mappings. (English) Zbl 1329.54057
Let \(A\) and \(B\) be two nonempty closed subsets of a complete metric space \((X,d)\) with \(A\cap B\neq\emptyset\) and let \(F: X\times X\to X\) be a mapping such that \(F(A\times B)\subset B\), \(F(B\times A)\subset A\) and, for some \(q\in(0,1)\) and all \(x,y,u,v\in X\),
\[
d(F(x,y),F(u,v))\leq q\max\left\{d(x,u),\frac12d(u,F(x,y)),\frac12d(x,F(u,v)), \frac12[d(x,F(x,y))+d(u,F(u,v))]\right\}.
\]
The author proves that \(F\) has a coupled fixed point in \(A\cap B\). No example is given.
Reviewer: Zoran Kadelburg (Beograd)
MSC:
54H25 | Fixed-point and coincidence theorems (topological aspects) |
54E40 | Special maps on metric spaces |
54E50 | Complete metric spaces |
References:
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