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Zbl 1210.54049
Abbas, Mujahid; Nazir, Talat; Radenović, Stojan
Some periodic point results in generalized metric spaces. (English)
[J] Appl. Math. Comput. 217, No. 8, 4094-4099 (2010). ISSN 0096-3003

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 $G(x,y,z)$ is defined for every $x$, $y$ and $z$ in $X$ and five axioms are assumed. Then $d(x,y)= G(x,y,y)+ G(y,x,x)$ 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.
[Lech Górniewicz (Toruń)]

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: fixed point; periodic point; generalized metric space

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