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In this paper, necessary and sufficient conditions that the real doubly infinite matrixA sums every strongly almost convergent double sequence, leaving the limit invariant, have been determined.
We introduce the concept of double uniform density of subsets of ℕ×ℕ and the study the corresponding convergence (namely, I u-convergence) of double sequences. Further we solve an inequality related to the I u-limit superior of bounded double sequences in line of [5].
In this paper we define and characterize the almost regular matrices for double sequences and further we apply these matrices to establish a core theorem.
Abstract
The main object of the present paper is to show that analogue of the Tauberian theorem for almost convergence is false for absolute almost convergence. Besides, applications are made for Fourier series.
Abstract
The idea of A-invariant mean and A-almost convergence is due to J. P. Duran [8], which is a generalization of the usual notion of Banach limit and almost convergence. In this paper, we discuss some important properties of this method and prove that the space F(A) of A-almost convergent sequences is a BK space with ‖ · ‖∞, and also show that it is a nonseparable closed subspace of the space l ∞ of bounded sequences.
