Sentence examples for in view of example from inspiring English sources

In view of Example 2.5, we remark that commuting mappings are weakly uniformly contraction mappings.

Remark 4.5 Corollary 4.1 (in view of Example 3.1) generalizes the results of Miheţ [[25], Theorem 3.1].

Clearly, weakly commuting mappings are compatible, but in view of Example 2.9 the converse does not hold.

Remark 4.4 Theorem 4.1 and Theorem 4.3 (in view of Example 3.1) improve and generalize the results of Mishra et al. [[4], Theorem 1].

In view of Example 2 and (i) of Remark 4, Theorem 2 is a particular case of Theorem 5 with (psi(t)=e^{t}inPhi_{2}).

If x = 1 and y ∈ ( 1, 3 2 ), then we have |T × − Ty| > 4|x − y| because of 0 < | x - y | < 1 2. But, in view of Example 2.18, T is a nearly uniformly 4-Lipschitzian mapping.

Earlier proved results can also be described in view of Examples 3.1-3.3 3.1-3.3Lemma 5.1) which improve the resusingof Chauhan and Kumar [[20], Theorem 4.1].

In view of this example, it's not difficult to imagine that using Google Earth maps may reveal additional pockets of biodiversity, especially in areas like Mozambique or, in my favourite part of the world, Papua New Guinea.

Inclusion is strict in view of the example cited in Theorem 3.1.

The inclusion is strict in view of the example cited in Theorem 3.2 as ( x k ) ∈ [ S ( b ) ] β for 1 2 < β ≤ 1, but ( x k ) ∉ [ S ( b ) ] α for 0 < α ≤ 1 2. □.

In view of the Example 2.3 in Qin et al. [41], we find that (J + r i ∂f i )-1J is closed quasi-ϕ-nonexpansive with F((J+ r i ∂f i )-1J) = (∂f i )-1 0).