Sentence examples for assures the existence from inspiring English sources

The following lemma assures the existence of stationary point.

Furthermore, condition (3.28) assures the existence of a matrix function such that condition (3.18) is fulfilled.

We note that Proposition 2.2 ii) assures the existence and uniqueness of.

Anderson ([1972]) assures the existence of a solution for r≤N/2.

The continuity of f assures the existence of x", z" ∈ [x', z'], x" < z", such that f(x") = f z") and z" - x" = y - x'.

This theorem assures the existence and uniqueness of fixed points of certain self-maps of metric spaces, and it gives a constructive method to find those fixed points.

In this case, the main point is to assure the existence of nontrivial solutions.

Energy dispersive X-ray spectroscopy (EDX) assured the existence of both iron and gold elements in the prepared nanoparticles.

Here, we assume (theta _{H} - frac {eta }{1 + eta }PDelta theta > 0) to assure the existence of an interior solution.

But, best proximity point theorems provide sufficient conditions that assure the existence of approximate solutions which are optimal as well.

The goal of best proximity point theory is to furnish sufficient conditions that assure the existence of such points.