Sentence examples for in view of the monotonicity from inspiring English sources

Assume that Then, in view of the monotonicity of (2.26).

By using induction, we can show that for all Assume that Then, in view of the monotonicity of, we have (2.27).

Then, in view of the monotonicity of T, T n ( Z ) is comparable to T n ( Z ∗ ) = Z ∗ and T n ( Z ¯ ) = Z ¯.

In view of the monotonicity of T, and the restriction (a), we obtain from (A4) 〈 y t − w, T y t 〉 ≥ F ( y t, q ).

Then, in view of the monotonicity of T, T n ( Z ) is comparable to T n ( Z ∗ ) = Z ∗ and to T n ( Z ¯ ) = Z ¯.

In view of the monotonicity of A 3, and the restriction (a), we obtain from (A4) that 〈 y t − q, A 3 y t 〉 ≥ F ( y t, q ).

In view of the concepts of monotonicities given by Al-Homidan et al. [20], we introduce ((alpha, rho, eta ))-monotonicity for a real-valued function, which will be helpful in proving our results.

Remark 10 In view of almost monotonicity and the existence of an asymptotic inversion for RV functions with a nonzero index, many of our considerations could be extended to nonlinearities F and G which are not necessarily (eventually) monotone.

We accentuate those which deal with this relation in view of superadditivity and monotonicity of the Jensen-type functionals, in [8, 9] or [10], obtained via [11] and suitably summarized in the monograph [12].

Indeed (2) implies that there exist a and (b, a < bar{x} < b) such that (f a, a) > a), (f(b, b) < b), which in view of monotonicity of f implies that f:[a,b] times[a,b]rightarrow[a,b], and so all conditions of Theorem 2 are satisfied.

In view of Definition 3.1, we note that the relaxed cocoercivity condition is weaker than the strong monotonicity condition.