Statistical convergence in g-metric spaces

Abstract

The purpose of this paper is to define statistically convergent sequences with respect to the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties of this statistical form of convergence.Definition 1.1. [14] Let X be a nonempty set and Let G : X × X × X → R + , be a function satisfying: 1) G(x, y, z) = 0 if x = y = z, 2) 0 < G(x, x, y); for all x, y ∈ X , with x = y, 3) G(x, x, y) G(x, y, z) , for all x, y, z ∈ X with z = y, 4) G(x, y, z) = G(x, z, y) = G(y, z, x) = ... , (symmetry in all three variables),