Sentence examples for mapping is maximal from inspiring English sources

Then the mapping is maximal monotone.

Equivalently, a monotone mapping is maximal monotone if for all, where denotes the range of.

It is well known that a monotone mapping is maximal if and only if for, for every implies.  .

We have already mentioned that in this case the mapping is maximal monotone, and if and only if.

It is well known that a monotone mapping is maximal if and only if for, for every implies.

It is known that a monotone mapping is maximal if and only if for, for every implies.

Let the set-valued mapping be maximal monotone.

We usually use a property of the maximal monotone mapping: A monotone mapping B is maximal if and only if for ((x,u in Htimes H), (langle x-y, u-vranglegeq0) for each ((y,v in G(B)) implies (uin Bx).

A monotone mapping M is maximal if the (operatorname{Graph}(M)) is not properly contained in the graph of any other monotone mapping.

It is known that a monotone mapping B is maximal if and only if, for any ( x, f ) ∈ H × H, 〈 x − y, f − g 〉 ≥ 0, for all ( y, g ) ∈ Graph ( B ) implies f ∈ B x.

By the Rockafellar theorem [25] (cf. [26]), the subdifferential mapping ∂f is maximal monotone in H. So, x_{n+1}=mathop{operatorname{argmin}}limits_{zin H} biggl{ f z)+ frac{1}{2}|z-y_{n}| ^{2} biggr} is equivalent to (partial f(x_{n+1})+x_{n+1}ni y_{n}).