Sentence examples for therefore as claimed from inspiring English sources

Therefore, as claimed (4.19) holds.

Therefore, (i) holds, as claimed.

Therefore, (lambda=0) is impossible, and we must have that (lambda>0), as claimed.

Therefore ({x_{n}}) converges strongly to a common fixed point q of the maps (T_{i}), as claimed.

as claimed.

Hence, as claimed.

Clearly, f(K) ⊂ K. Closed convex sets are weakly closed [6, Theorem V.3.18] and therefore K is weakly compact, as claimed.

Therefore f ( x ∗ ) = y ∗, as claimed.

Therefore, the equilibrium point (tilde{X}^) is locally asymptotically stable as claimed.

Therefore, R f ( a, b ) ≥ R g ( a, b ) = L, as claimed.

Therefore \(S \cap X\ne \varnothing\); and \(S\) is a sampling as claimed.