Abstract
Inspired by the notion of Mustafa and Sims’ G-metric space and the attention that this kind of metric has received in recent times, we introduce the concept of a G-metric space in any number of variables, and we study some of the basic properties. Then we prove that the family of this kind of metric is closed under finite products. Finally, we show some fixed-point theorems that improve and extend some well-known results in this field. MSC:46T99, 47H10, 47H09, 54H25.
Highlights
1 Introduction In the s, Gähler [, ] tried to generalize the notion of metric and introduced the concept of -metric spaces inspired by the mapping that associated the area of a triangle to its three vertices
The main aim of the present paper is to introduce the notion of a G-metric space in any number of variables
We prove two relevant facts: the product of metrics of this kind is a metric in this sense, and there is no a trivially way to reduce the number of variables
Summary
In the s, Gähler [ , ] tried to generalize the notion of metric and introduced the concept of -metric spaces inspired by the mapping that associated the area of a triangle to its three vertices. Definition Let (X, G) be a Gn∗-metric space, let {xm} ⊆ X be a sequence and let x ∈ X be a point.
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