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Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition. (English) Zbl 1133.54024
Let \(X\) be a metric space. A mapping \(T: X \mapsto X\) is called weakly contractive with respect to \(f:X \mapsto X\) if for each \(x, y\in X,\) \[ d(Tx,Ty)\leq d(fx,fy)-\varphi d(fx, fy) \] where \(\varphi :[0,+\infty )\rightarrow [0,+\infty )\) is continuous, nondecreasing, positive on \((0,+\infty )\), \(\varphi(0)=0\) and \(\lim_{t\rightarrow \infty}\varphi(t)=\infty\).
The authors prove the existence of coincidence points and common fixed points for a weakly contractive mapping \(T\) with respect to \(f\). Related results on invariant approximation are also derived.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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