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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(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.
54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces
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