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Zbl 1164.54030
Ćirić, L.B.; Prešić, S.B.
On Prešić type generalization of the Banach contraction mapping principle. (English)
[J] Acta Math. Univ. Comen., New Ser. 76, No. 2, 143-147 (2007). ISSN 0862-9544

The paper generalizes some previous results of the second author. Let $(X,d)$ be a metric space, $k$ a positive integer and $T$ a mapping of $X^k$ into $X$. The authors show that if $T$ satisfies certain contractive type conditions and, on diagonal $\delta \subset X^k$, $d\bigl (T(u,\dots ,u),T(v,\dots ,v)\bigr ) < d(u,v)$ holds for all $u, v \in X$ with $u \ne v$, then there exists a unique $x \in X$ such that $T(x,x,\dots ,x) =x$.
[L\!'ubica Holá (Bratislava)]

MSC 2000:: *54H25 Fixed-point theorems in topological spaces

Keywords: fixed point; Cauchy sequence; complete metric space

Cited in: Zbl pre06127590

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