Sentence examples for a sequence of strongly from inspiring English sources

Let be a sequence of strongly mixing random variables with zero mean, and let be a triangular array of real numbers.

Let { T n } or { S n } be a sequence of strongly nonexpansive mappings, and let f : C → C be a contractive mapping with α ∈ ( 0, 1 2 ).

Let X be a left invariant φ-stable subspace of L ∞ containing 1, { μ n } n = 1 ∞ be a sequence of left strongly asymptotically invariant means defined on X such that lim n → ∞ ∥ μ n + 1 − μ n ∥ = 0 and { c n } n = 1 ∞ be the sequence defined by c n = sup x, y ∈ C ( ∥ T μ n x − T μ n y ∥ − ∥ x − y ∥ ), n ≥ 1.

From the definition of strongly mixing we know that remain to be a sequence of identically distributed strongly mixing random variable with zero mean and unit variance.

In the first case, we obtain an unbounded sequence of solutions (Theorem 3.1); in the second case, we obtain a sequence of nonzero solutions strongly converging at zero (Theorem 3.4), which improve and extend the results in [10].

It is easily seen that the partial sum of a sequence of mean zero strongly positive dependent random variables is also a demimartingale by the inequality (3) in Zheng [7], that is, for all, (1.5).

Let { T n } n = 1 ∞ be a sequence of left Bregman strongly nonexpansive mappings onCsuch that F ( T n ) = F ^ ( T n ) for alln ≥ 0 and Ω : = ( ∩ n = 1 ∞ F ( T n ) ) ∩ ( ∩ j = 1 N E P ( g j ) ) ≠ ∅.

Let T i ( i = 1, 2, …, m ) be a sequence of left Bregman strongly nonexpansive mappings onCsuch that F ( T i ) = F ^ ( T i ) for alln ≥ 0 and Ω : = ( ∩ i = 1 m F ( T i ) ) ∩ ( ∩ j = 1 N E P ( g j ) ) ≠ ∅.

Let be a sequence of identically distributed positive strongly mixing random variable with and,,.

Let be a sequence of identically distributed positive strongly mixing random variable with and, and as mentioned above.

In this section, we introduce a new iterative scheme and prove that a sequence of our scheme converges strongly to a solution of a Hammerstein equation under this setting.