Sentence examples for mapping as desired from inspiring English sources

Thus A : X → Y is an additive mapping, as desired.

Hence the mapping is the unique bi-quadratic mapping, as desired.

Hence the mapping is the unique 2-dimensional vector variable quadratic mapping, as desired.

Hence Q : X → Y is an orthogonally quadratic mapping, as desired.

By [32], Lemma 2.2], A : Y → X is an additive mapping, as desired.

By [32], Lemma 2.2], A : X → Y is an additive mapping, as desired.

Thus L : X → Y is a unique orthogonally additive mapping satisfying (5), as desired.

Hence, Q : X → Y is a unique orthogonally quadratic mapping satisfying (1), as desired.

Thus L: X → Y is a unique orthogonally additive-additive mapping satisfying (2.3), as desired.

Thus A : Y → X is a unique additive mapping satisfying (2.8), as desired.

Therefore, there exists a unique additive mapping satisfying (2.28), as desired.