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Some periodic point results in generalized metric spaces. (English) Zbl 1210.54049
The authors consider a class of spaces called generalized metric spaces. The metric $G$ is defined for any three points $x$, $y$, $z$ of the set $X$, i.e., a nonnegative real number $G\left(x,y,z\right)$ is defined for every $x$, $y$ and $z$ in $X$ and five axioms are assumed. Then $d\left(x,y\right)=G\left(x,y,y\right)+G\left(y,x,x\right)$ is a metric induced by $G$. Let me add that the notion of $G$-metric space considered in this paper is only formally new. The same holds for the notion of contractive mapping with respect to the generalized metric $G$. Finally three fixed point theorems for such $G$-contractions are proved.
##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces 47H10 Fixed point theorems for nonlinear operators on topological linear spaces
##### Keywords:
fixed point; periodic point; generalized metric space
##### References:
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