Lacunary A- Convergence

In this paper we introduce the concept of LacunarySummability. We also give the relations between these summability and Lacunary statistical Summability. Following the concept of statistical limit superior and inferior, we give a definition of Lacunary limit superior and inferior which yields natural relationships among these ideas: x is Lacunary convergent if and only if Lacunary core of is also introduced and it is proved that a bounded sequence that summable to its Lacunary limit superior is Lacunary convergent.