Sentence examples for be an -proximal mapping from inspiring English sources

then the mapping, denoted by, is said to be an -proximal mapping of with respect to.

where is the -proximal mapping of with respect to and is a constant.

that is, and the -proximal mapping of is well defined.

that is, and the -proximal mapping of with respect to is well defined.

If is -subdifferentiable at each, then is -subdifferentiable and the -proximal mapping of with respect to is -Lipschitz continuous.

Suppose that (T : Arightarrow B ) is a proximal contraction mapping such that (T(A_{0} )subseteq B_{0}) and (g : Arightarrow A ) is an isometry mapping such that (A_{0}subseteq g(A_{0}) ).

Suppose that (T : Arightarrow B ) is a proximal nonexpansive mapping such that (T(A_{0} )subseteq B_{0}) and (g : Arightarrow A ) is an isometry mapping such that (A_{0}subseteq g(A_{0}) ).

If (T : Arightarrow B ) is a proximal nonexpansive mapping such that (T(A_{0} )subseteq B_{0}) and (g : Arightarrow A ) is an isometry mapping such that (A_{0}subseteq g(A_{0}) ), then there exists an element (xin A_{0} ) such that (nu_{gx - Tx}(t)=nu_{A-B}(t)) for all (t>0).

Suppose that (T : Arightarrow B ) is a continuous affine and proximal nonexpansive mapping such that (T(A_{0} )subseteq B_{0}) and (g : Arightarrow A ) is an isometry mapping such that (A_{0}subseteq g(A_{0}) ).

Furthermore, if the subdifferential for is -strongly monotone, then the -proximal mapping is -Lipschitz continuous.

Furthermore, if additionally the -subdifferential for is -strongly monotone, then the -proximal mapping of with respect to is -Lipschitz continuous.