Sentence examples for valued operator from inspiring English sources

We denote a set valued operator U from E to E* by U ⊂ E × E*.

Since is a continuous single valued operator, it is clear that has nonempty, closed, and convex values.

Let (A Erightarrow E) be a single valued operator and let (B Erightarrow 2^{E}) be an m-accretive operator.

Since r ( x, ξ ) is a continuous and single valued operator, from Theorem 2 of [18], we know that r ( x, ξ ) is a weak continuous operator.

The subdifferential ∂f of f is the set valued operator, defined (partial f= {uin H: f y geq f(x)+langle y-x,urangletext{ for all } yin H}).

Definition 2.3 For i, j = 1, 2, …, m, let H i be a Hilbert space, A j : H j → H j be single-valued operator, U i j : H j → 2 H j be set-valued operator.

A monotone set-valued operator T is called maximal if its graph, Gph ( T ) : = { ( x, y ) ∈ H × H : y ∈ T ( x ) }, is not properly contained in the graph of any other monotone operator.

Let Y be a compact convex subset of a Banach space E and (T Yto P(Y)) be an upper semi-continuous multi-valued operator with acyclic values.

Let X be a nonempty closed subset of a Banach space E and (G: X to{mathcal{P}}(E)) be a multi-valued operator with nonempty closed values.

Let be a single-valued operator and let be a set-valued operator.

A single-valued operator is said to be.