Sentence examples for mapping defined in from inspiring English sources

We first characterize the solutions of the optimization problem as fixed-points of a mapping defined in terms of the gradient of the differentiable function and the proximity operators of the other two functions.

Then the mapping defined in (2.2) is the least Carathéodory solution of (1.1) and the mapping defined in (2.3) is the greatest one.

Recall the definition of an asymptotic pointwise nonexpansive mapping defined in metric spaces [10, 26].

Example 6.1 Let T 2 be a soft mapping defined in Example 5.5.

Recall the definition of a nonexpansive mapping defined in metric spaces.

where E is the end-point mapping defined in Definition 1.

The second part is an analogy to the Haldane map function defined in hidden Markov model [18].

Let F be the associated multivalued map defined in (3.3).

then the map defined in is a contraction.

Let be the map defined in the previous theorem.

Let Ψ, Φ and (F_{varepsilon}) be the maps defined in (3.3) and (3.4).