The σσ-convergence and σσ-core of double sequences

The σσ-convergence and σσ-core of a real bounded sequence were introduced in [R. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30 (1963) 81–94] and [S.L. Mishra, B. Satapathy, N. Rath, Invariant means and σσ-core, J. Indian Math. Soc. 60 (1984) 151–158], respectively. In this work, we extend these ideas to double sequences.