Sentence examples for increasing sequences and from inspiring English sources

In (1.1), { x n }, { y n } are monotonically increasing sequences and the positive equilibrium point of system (1.1) is unique, we get M = x ∗, N = y ∗.

In (A6), p, q, (2^{m}) can be defined as increasing sequences, and (zeta_{in}to0), (i=1,2,3,4), are easily satisfied, if p, q and (2^{m}) are chosen reasonable.

In this study, we have generalized a well-known theorem dealing with an absolute summability method to a ({varphi}-|T,p_{n}|_{k}) summability method of an infinite series by using almost increasing sequences and δ-quasi-monotone sequences.

To confirm the main results obtained in Theorem 6.3, we fixed the parameter values as those in Figure 8, and we can see that if (A_{h}>0), then the impulsive points and its phase points of trajectory shown in Figure 8(C) are two monotonically increasing sequences, and eventually the trajectory approaches a closed orbit which frees it from impulsive effects.

In 2014, Bor [7] generalized the (vert C, alpha vert _{k}) summability factor to the (vert C, alpha, beta delta vert _{k}) summability of an infinite series and in [8], he discussed a general class of power increasing sequences and absolute Riesz summability factors of an infinite series.

Let ( X n ) be an almost increasing sequence and ( φ n p n P n ) be a non-increasing sequence.

Let be an almost increasing sequence and let and be sequences such that.

For let be a increasing sequence and be a decreasing sequence.

Therefore,, that is, is an increasing sequence and, hence, the limit of exists.

Let ((Y_{n})) be an almost increasing sequence and (lambda_{n}rightarrow0) as (nrightarrowinfty).

Continue with this increasing sequence and eventually the least fixed point of \ [E]\) will be reached.