\(I_θ\)-STATISTICALLY CONVERGENT SEQUENCES IN TOPOLOGICAL GROUPS
Recently, Das, Savaş and Ghosal [4], defined the lacunary statistical analogue for the sequence \(x=(x_k)\) as follows: A real sequence \(x=(x_k)\) is said to be \(I\)-lacunary statistically convergent to \(L\) or \(S_θ^I \)-convergent to \(L\) if for any \(ε>0\) and \(δ>0\) \[ {rN:1h_r|{kI_r:|x_k-L|≥ε}|≥δ}I. \] In this case write \(S_θ^I -x=L\) or \(x_k→ L(S_θ^I )\). In this paper, we introduce and study \(I\)-lacunary statistical convergence for sequence in topological groups and we shall also present some inclusion theorems. , number=2, journal=Matematichki Bilten, author=Savaş, Ekrem, year=2015, month=Jan., pages=19–28