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In this paper, we study the concepts of invariant convergence, p-strongly invariant convergence [V 2 σ ]p  , I2-invariant convergence I σ 2  , I ∗ 2 - invariant convergence I σ∗ 2  of double sequences and investigate the relationships among invariant convergence, [V 2 σ ]p, I σ 2 and I σ∗ 2 . Also, we introduce the concepts of I σ 2 -Cauchy double sequence and I σ∗ 2 -Cauchy double sequen

On ideal invariant convergence of double sequences and some properties