Sentence examples for by a counter example from inspiring English sources

We prove the statement by a counter example.

We show by a counter example that rational dilation fails on the tetrablock, a polynomially convex and non-convex domain in C3 defined asE="{ x1,x2,x3)∈C3:1−zx1−wx2+zwx3≠0whenever |z|≤1,|w|≤1}.

end{aligned} (4d) Despite the scheme working very well for many concrete applications of (1) (see e.g. [1, 2, 4, 14]), Chen et al. [15] showed by a counter example that the convergence of (4a - 4d) fails.

Now by an counter example, we prove that the iteration process ARS n due to Agarwal et al. [3] is faster than the Mann and Ishikawa iteration processes for Zamfirescu operators.

Then M n and I n converge strongly to the unique fixed point of a Zamfirescu operator T : C → C, and, moreover, the Mann iteration process converges faster than the Ishikawa iteration process to the fixed point of T. Remark 7 In [18], Qing and Rhoades, by taking a counter example, showed that the Ishikawa iteration process is faster than the Mann iteration process for Zamfirescu operators.

We prove by showing a counter example, using the network in Figure 11.

In this note, by taking an counter example, we prove that the iteration process due to Agarwal et al. (J. Nonlinear Convex. Anal. 8 (1), 61-79, 2007) is faster than the Mann and Ishikawa iteration processes for Zamfirescu operators.

Next to the description of the algorithm, we prove, by means of a counter example, that an exact nonnegative decomposition of a general positive semidefinite matrix is not always available.

Note that strong convergence of these methods fails in general (see a counter example by Hundal [8]).

For a counter example, we refer to Example 4.1.

According to them moral beliefs stand as a counter example.