Sentence examples for be two positive sequences from inspiring English sources

Let {r n } and {s n } be two positive sequences and {α n }, {β n }, and {γ n } sequences in (0, 1).

Lemma 3.1 Let ( a n ) and ( b n ) be two positive nonincreasing sequences.

Let { r n } and { s n } be two positive real number sequences.

Let ((u_{n})) and ((v_{n})) be two positive non-decreasing sequences.

Let ((a_{n})) and ((b_{n})) be two positive non-increasing sequences.

Then (1.9) is reduced to the following: (1.10). is said to be  generalized asymptotically nonexpansive if there exist two positive sequences with and with as such that (1.11).

Hence, there are two positive integer sequences and satisfying (3.36).

where P K is the metric projection from H onto K, W n is a mapping defined by (2.5), { α n } is a real number sequence in ( 0, 1 ), and { λ n }, { η n } are two positive real number sequences.

Let ({g(n), ngeq1}) and ({f(n), ngeq1}) be two sequences of positive constants with (f(n)uparrowinfty) and ({Psi_{n}(t),ngeq1}) ba a sequence of even and nonnegative functions such that, for each (ngeq1), (Psi_{n}(t)>0) as (t>0).

Let (theta > 1), and let ({upsilon_{k}}) and ({gamma_{k}}) be two sequences of positive numbers with ({upsilon_{k}} toinfty).

Let (eta_{0}geqeta _{1}geqcdots) and (theta_{0}geqtheta_{1}geqcdots) be two sequences of positive numbers such that (eta_{k}downarrow0), (theta_{k}downarrow0) as (krightarrow+infty).