Adem, Abdu AwelAltinok, Maya2025-03-172025-03-1720200352-96652406-047Xhttps://doi.org/10.22190/FUM12003887Ahttps://hdl.handle.net/20.500.13099/1658Functions defined in the form g : N -> [0, infinity) such that lim(n ->infinity) g(n) = infinity and lim(n ->infinity) n/g(n) = 0n are called weight functions. Using the weight function, the concept of weighted density, which is a generalization of natural density, was defined by Balcerzak, Das, Filipczak and Swaczyna in the paper \Generalized kinsd of density and the associated ideals, Acta Mathematica Hungarica 147(1) (2015), 97-115. In this study, the definitions of g-statistical convergence and g-statistical Cauchy sequence for any weight function g are given and it is proved that these two concepts are equivalent. Also, some inclusions of the sets of all weight g(1)-statistical convergent and weight g(2)-statistical convergent sequences for g(1), g(2) which have the initial conditions are given.eninfo:eu-repo/semantics/closedAccessweight functionsnatural densitystatistical convergent sequencesArticle10.22190/FUM12003887A353887898N/AWOS:000585969100022N/A