The purpose of this paper is to define statistically convergent sequences with respect the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties statistical form convergence.

In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and Cauchy sequence. this paper, we define $A^{I^{\ast }}$-statistical find under certain conditions, that it is equivalent to $A^{I}$-statistical defined in [Appl. Math. Lett. 2012, 25 733-738]. Moreover, $A^{I}$- sequences some with convergence.

In this paper, we are dealing with Cheney-Sharma Chlodovsky Durrmeyer operators and studying their approximation properties. The Bohman-Korovkin theorem is verified estimated the convergence properties using of modulus continuity, Lipschitz- type space, Ditzian-Totik continuity. After that, weighted result also given. Finally, some results related to A-statistical o...