Sentence examples for are proven using the from inspiring English sources

The stability and convergence of the scheme are proven using the discrete energy method.

Linear and non-linear stability results, including A-stability, L-stability and B-stability are proven using the energy method for general initial value problems.

Moreover, the PPF dependent fixed point theorems for mappings satisfying some generalized contractive conditions in partially ordered Banach spaces are proven using the mentioned properties for Ψ 1 and Ψ 2. Suppose that E is a real Banach space with the norm ∥ ⋅ ∥ E and I is a closed interval [ a, b ] in ℝ.

Some of our results are proved using the next well-known results.

The unconditional stability and the high-order convergence are proved using the Fourier analysis method.

Robustness and convergence of the proposed schemes are proved using the second method of Lyapunov and the super-twisting algorithm.

In this paper, inequalities for convex combinations of functionals satisfying conditions (a) and (b) are formulated in the theorems, and some corollaries are proved, using the theorems.

The stability of the developed controller is proven, using the theory of Lyapunov.

The stability of the closed-loop system is proven using the Lyapunov Krasovskii functions.

The stability of the EASFSC has been proven using the Lyapunov stability theorem.

In addition, the stability of the guidance system is proven using the Lyapunov theorem.