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^2_sigma ]_p), I2-invariant convergence (I_sigma^2), I*_2 -invariant convergence (I_2*^sigma) of double sequences and investigate the relationships among invariant convergence, [V^2_sigma ]p, I*_2 and (I_2*^sigma). Also, we introduce the concepts ofI_sigma^2 -Cauchy double sequence and I_2*^sigma -Cauchy double sequence.