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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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