Sentence examples for maximal iff for from inspiring English sources

It is known that a monotone mapping Q is maximal iff for ( x, f ) ∈ E × E ∗, 〈 x − y, f − g 〉 ≥ 0 for every ( y, g ) ∈ Graph ( Q ) implies f ∈ Q x.

It is clear that a monotone mapping T is maximal iff for any ((x,u in Htimes H), if (langle u-v,x-yranglegeq0), (forall y,v in G(T)), then it follows that (uin T x)).

It is known that a monotone mapping S is maximal iff for ( x, f ) ∈ H × H, 〈 x − y, f − g 〉 ≥ 0 for every ( y, g ) ∈ G ( S ) implies f ∈ S x.

It is known that a monotone mapping S is maximal iff for ( x, f ) ∈ H × H, 〈 x − y, f − g 〉 ≥ 0 for every ( y, g ) ∈ Graph ( S ) implies f ∈ S x.

It is well known that a monotone mapping T is maximal iff, for any ((x,f in Htimes H), (langle x-y,f-granglegeq0) for all ((y,g in G(T)) implies (fin Tx).

A set-valued mapping R : H ⇉ H is said to be monotone iff, for all x, y ∈ H, f ∈ Rx and g ∈ Ry imply 〈x - y, f - g〉 > 0. A monotone mapping R : H ⇉ H is maximal iff the graph G(R) of R is not properly contained in the graph of any other monotone mapping.

Recall that a set-valued mapping M H ⇉ ⇉ H is said to be monotone iff, for all x, y ∈ H, f ∈ M x, and g ∈ M y imply 〈 x − y, f − g 〉 > 0. M is maximal iff the graph Graph ( M ) of R is not properly contained in the graph of any other monotone mapping.

Recall that a set-valued mapping M : H ⇉ H is said to be monotone iff, for all x, y ∈ H, f ∈ M x and g ∈ M y imply 〈 x − y, f − g 〉 > 0. A monotone mapping M : H ⇉ H is maximal iff the graph Graph ( M ) of R is not properly contained in the graph of any other monotone mapping.

Recall that a set-valued mapping B : H ⇉ H is said to be monotone iff, for all x, y ∈ H, f ∈ B x and g ∈ B y imply 〈 x − y, f − g 〉 > 0. In this paper, we use B − 1 ( 0 ) to stand for the zero point of B. A monotone mapping B : H ⇉ H is maximal iff the graph Graph ( B ) of B is not properly contained in the graph of any other monotone mapping.

A monotone operator B on H is said to be maximal iff its graph is not strictly contained in the graph of any other monotone operator on H.

A replica o i is maximal iff there is no replica o j in the quorum Q such that o i ≼ o j.