Glasnik Matematicki, Vol. 45, No.1 (2010), 139-153.

SOME NEW DOUBLE SEQUENCE SPACES OF INVARIANT MEANS

M. Mursaleen and S. A. Mohiuddine

Abstract.   In this paper, we define some new spaces of double sequences involving the idea of σ-mean; i.e., we define the spaces of strongly σ-convergent, absolutely σ-almost convergent, σ-almost bounded and absolutely σ-convergent double sequences and establish some inclusion relations along with some numerical examples.

2000 Mathematics Subject Classification.   40C05, 40H05.

Key words and phrases.   Double sequences, absolute almost convergence, σ-mean, strong σ-convergence, absolute σ-convergence, σ-almost boundedness, absolute σ-convergence.

DOI: 10.3336/gm.45.1.11

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