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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.
Keywords:
fixed point
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