Lacunary I_2-invariant convergence and some properties

In this paper, the concept of lacunary invariant uniform density of any subset A of the set N×N is defined. Associate with this, the concept of lacunary I_2-invariant convergence for double sequences is given. Also, we examine relationships between this new type convergence concept and the concepts of lacunary invariant convergence and p-strongly lacunary invariant convergence of double sequences. Finally, introducing lacunary I_2^∗-invariant convergence concept and lacunary I_2-invariant Cauchy concepts, we give the relationships among these concepts and relationships with lacunary I_2-invariant convergence concep