Sentence examples for proven under suitable from inspiring English sources

In [3], it is proven, under suitable conditions, that such a vector field (mathbf {v}_t) must belong to what is defined as the Wasserstein sub-differential of the functional F, provided in particular that F is (lambda )-convex.

Next, a strong convergence theorem of the proposed algorithm is proved under suitable conditions.

A strong convergence theorem of the sequence generated by our iterative scheme is proved under suitable conditions.

We prove, under suitable conditions on α, β, m, p and for negative initial energy, a global nonexistence of solutions.

An equivalence result concerned with two classes of -generalized vector variational-like inequalities is proved under suitable conditions.

In Section 2 the existence and uniqueness of the solution to the identification problems ((mathcal{IP}1 )) and ((mathcal{IP}2)) are proved under suitable assumptions on the data.

In this paper, the existence of ε-approximate equilibrium points for a bifunction is proved under suitable conditions in the framework of a Hadamard space.

This fact does not prevent progress from being made on the topic; for if one's aim is to establish no-go results for time machines it suffices to identify necessary conditions for the operation of a time machine and then to prove, under suitable hypotheses about what is physically possible, that it is not physically possible to satisfy said necessary conditions.

In this paper, a general iterative scheme for approximating a point of F ( T ) ∩ ( A + B ) − 1 0 ∩ G − 1 0 ≠ ∅ is introduced, where F ( T ) is the set of fixed points of T, and a strong convergence theorem of the sequence generated by the iterative scheme is proved under suitable conditions.

Global convergence of the proposed method is proven under some suitable conditions.

It is proven that under suitable conditions, the sequences generated by the proposed iterative algorithms converge weakly to a solution of the split feasibility and fixed point problems.