I_2-statistically and I_2-lacunary statistically convergent double set sequences of order η

Abstract

In this study, for double set sequences, as a new approach to the notion of statistical convergence of order η, the notions of Wijsman I_2-statistically convergence of order η, Wijsman strong I_2-Ces`aro summability of order η, Wijsman I_2-lacunary statistically convergence of order η and Wijsman strong I_2-lacunary summability of order η are introduced, where 0 < η ≤ 1. Also, some properties of these notions are investigated, some investigations about these are made and the existence of some relationships between them are examined.