Sentence examples for be proved by continuity from inspiring English sources

(2.51) The integral equation (2.51) is still valid for (x = y ), this can be proved by continuity of ({ K x,y leq Csigma ( frac{x+y}{2} )} ) and the continuity of (H xi)) in the metric (L_{2}(2,infty)).

The continuity of ρ can be proved by a standard argument from the theory of hyperbolic equations.

The existence and regularity of the unique solution w can be proved by applying classical methods, for instance, the method of continuity (see [29]).

The time-continuity of the solution (ρ, u, w) can be proved by the same argument as in Section 2. This completes the proof of Proposition 3.1.

Subsequently, several common fixed point theorems have been proved by combining the ideas of R-weakly commuting mappings and reciprocal continuity of mappings in different settings.

The non-negativity of R ( t ) ∀ t ∈ [ 0, t f ] is proven by using continuity arguments.

"These practices have been proven by time".

The theorem was proven by Boris Trakhtenbrot (1950).

All recurrences were proven by biopsy.

Metastases were proven by biopsy.

CFSGS was proven by biopsy.