On ideal invariant convergence of double sequences and some properties

Abstract

In this paper, we study the concepts of invariant convergence, p-strongly invariant convergence ([V_2σ ]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 Iσ∗2. Also, we introduce the concepts of Iσ2-Cauchy double sequence and Iσ∗2-Cauchy double sequences.