Sentence examples for a easy consequence of from inspiring English sources

Here we have used the fact that (B psi,x_{k-1},x_{k}) in L theta _psi )) for some (,theta _psi =(theta _psi ^-,theta _psi ^+)in (0,,pi ]^2), which is a easy consequence of Proposition 13, the inequality (,psi >0,) in (, x_{k-1}, x_{k-1}nd the above inequality.

A correct formula is an easy consequence of the results of Section 5 of [4].

and as an easy consequence of Lemma 2.6(a), and for each.

As an easy consequence of this theorem, we present now a result about existence of solutions for the second order difference problem (1).

We now draw an easy consequence of Eq. (4), which will play a major role in the following analysis.

(4) It is an easy consequence of items 2 and 3 since { A m } G -Cauchy ⇔ each  { a m i } G -Cauchy ⇔ each  { a m i } G -convergent ⇔ { A m } G -convergent.

Hence z is a common fixed point of mappings A, B, S and T. Uniqueness of common fixed point is an easy consequence of the inequality (5.3).

Therefore, z is a common fixed point of the mappings A, B, S and T. The uniqueness of common fixed point is an easy consequence of the inequality (4.1) in view of ( ϕ 1 ) and ( ϕ 2 ).

In this paper we observe that if M ⊆ X 4 is F-invariant and has the transitive property, we could induce a preorder on X 2 such that Theorem 11 can be seen as an easy consequence of Theorem 5.

The following result is an easy consequence of Theorem 1. Corollary 1 Let ( X, d ) be a complete metric space endowed with a graph G and f : X → X be a ( G, ψ ) -contraction, then the following statements are equivalent: (i) G is weakly connected;   (ii) there is x ∗ ∈ X such that lim n → ∞ f n x = x ∗, for all x ∈ X.  .

Uniqueness of is an easy consequence of (3.5).