Sentence examples for be strongly superlinear if from inspiring English sources

and are said to be strongly superlinear if there exist constants and with, such that and are nondecreasing with respect to for each fixed.

The function is said to be strongly superlinear if there exists, such that is a nondecreasing function with respect to for each fixed.

Φ : K → K is said to be strongly superlinear, if for ∀ x > 0 and t ∈ ( 0, 1 ), one has Φ ( t x ) ≪ t Φ x.

It is easy to see that the function is nondecreasing with respect to for if is strongly superlinear.

If and are strongly superlinear (i.e., ), then a necessary and sufficient condition for (1.1) to oscillate is that (2.26).

If Φ : K → K is strongly superlinear and increasing, then Φ has at most one positive fixed point.

Therefore, Φ is strongly superlinear.

where,, and are strongly superlinear or sublinear functions.

It is easy to see that is strongly superlinear for and is strongly sublinear for.

We establish some necessary and sufficient conditions for oscillation of the solutions of the following two-dimensional difference system:,, where and are strongly superlinear or sublinear functions.

The results can be extended easily to equations of the form x Δ n t + f t, x ξ t = 0, when f : T × ℝ → ℝ is continuous and f is strongly superlinear or f is strongly sublinear, see [4].