Sentence examples for well posed with from inspiring English sources

This means that (u_{k}) should be well posed with respect to (w_{0}), which is called the well-posed condition of iterative functions, that is, c_{1} e) biglvert nabla u_{k} e) bigrvert ^{p-2} le biglvert nabla w_{0} e) bigrvert le c_{2} e) biglvert nabla u_{k} e) bigrvert ^{p-2}, (3.6) where (c_{1} e)) and (c_{2} e)) meet the requirements of Definition 2.

Then the fixed point problem for f is well posed with respect to d.

Therefore, the fixed point equation (1.1) is well posed with respect to α. □.

It was shown that the CH2 system is locally well posed with initial data ( u 0, ρ 0 ) ∈ H s × H s − 1, s > 3 2 [18].

(ii If (VQVI) is type I (resp., type II) LP well posed, (P) is type I (resp., type II) LP well posed with defined by (2.14).

So (VQVI) is generalized type I (resp., generalized type II) LP well posed if and only if (P) is generalized type I (resp., generalized type II) LP well posed with defined by (2.26).

Moreover, from (a1) and (a2), that is, (operatorname{Fix}(T) = Soperatorname{Fix}(T) = {z}), we deduce that if the fixed point problem is well posed for T with respect to p, then it is well posed for T with respect to (H_{p}).

(operatorname{Fix}(T) = Soperatorname{Fix}(T) = {z }); the fixed point problem is well posed for T with respect to (H_{p}) if (s >1).

Then: (a) (operatorname{Fix}(T) = Soperatorname{Fix}(T) = {z });   (b) the fixed point problem is well posed for T with respect to (H_{p}) if (s >1).  .

In these conditions the fixed point problem is well posed for T with respect to H. Proof From (i) and (ii) we obtain that S Fix ( T ) = { x ∗ }.

Then the fixed point problem is well posed for T with respect to (H_{p}) if: (a2):  (Soperatorname{Fix}(T) = {z}); (b2):  if (x_{n} in X), (n inmathbb{N}) and (lim_{nrightarrow+infty}H_{p}(x_{n},Tx_{n}) = 0), then (lim_{nrightarrow+infty}p(x_{n},z) = 0).