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Quasi contraction non-self mappings on Banach spaces. (English) Zbl 1261.47070
The author proves that, if $$C$$ is a nonempty closed subset of a Banach space $$X$$, then a mapping $$T:C\to X$$ has a unique fixed point if it maps the boundary of $$C$$ into $$C$$ and satisfies $d(Tx,Ty)\leq kM(x,y),$ where $$0<k<1$$ and $M(x,y)=\max\{d(x,y),d(x,Tx),d(y,Ty),d(x,Ty),d(y,Tx)\}.$

##### MSC:
 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
fixed point