Sentence examples for be a double sequence from inspiring English sources

A sequence is said to be a double sequence of.

Let be a double sequence of positive real numbers with, and let.

Let λ be a double sequence space converging with respect to some linear convergence rule (varthetambox lim:lambdatomathbb {C}).

Theorem 3.7 Let I be an admissible ideal and x = ( x j k ) be a double sequence.

Let λ be a double sequence space and converging with respect to some linear convergence rule is (vartheta-lim:lambdato mathbb{C}).

A double sequence space E is said to be solid if { x k, l y k, l } ∈ E for all double sequences { y k, l } of scalars such that | y k, l | < 1 for all k, l ∈ N whenever { x k, l } ∈ E. Let x = { x k, l } be a double sequence.

Suppose that is a double sequence satisfying (2.4) for some and Then it is clear that.

If x = ( x j k ) is a double sequence in X such that I F - lim x = ℓ, then I F ∗ - lim x = ℓ.

An FDK-space is a double sequence space endowed with a complete metrizable space, locally convex topology under which the coordinate mappings x = ( x k ) → ( x mn ) ( m, n ∈ N ) Open image in new window are also continuous.

Also the following Tauberian results are proved: if (x=(x_{m,n})) is a double sequence that is mapped into (ell_{2}) by the four-dimensional Borel method and the double sequence x satisfies (sum_{m=0}^{infty}sum_{n=0}^{infty}|Delta_{10} x_{m,n}|sqrt {mn}

In this paper, we introduce two new inequalities with a best constant factor which gives an upper estimate for the double series ∑ n = 1 ∞ ∑ m = 1 ∞ σ n, m and the double integral ∫ 0 ∞ ∫ 0 ∞ G ( x, y ) d x d y, where σ n, m is a double sequence of positive numbers and G ( x, y ) is a positive function on ( 0, ∞ ) × ( 0, ∞ ).