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Lacunary Arithmetic convergence

In this article we introduce and study the lacunary arithmetic convergent sequence space $AC_θ$. Using the idea of strong Cesàro summable sequence and arithmetic convergence we define $AC_{σ_1}$ and study the relations between $AC_θ$ and $AC_{σ_1}$. Finally using modulus function we define $AC_θ(f)$ and study some interesting results.