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Common fixed points of \(f\)-weak contractions in cone metric spaces. (English) Zbl 1304.54096

Let \((X,d)\) be a cone metric space over a regular cone \(P\), with \(d(x,y)\in\text{int}P\) for \(x\neq y\), and let \(f,T:X\to X\) be two mappings satisfying \(d(Tx,Ty)\preceq d(fx,fy)-\phi(d(fx,fy))\) for \(x,y\in X\), where \(\phi:\text{int}P\cup\{0\}\to\text{int}P\cup\{0\}\) satisfies certain conditions. The authors prove a coincidence point and a common fixed point result for \(f\) and \(T\).

MSC:

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