Sentence examples for bounded functional such that from inspiring English sources

Let (f:Erightarrow -infty,infty]) bErightarrow -inftytinuously Frèchet differentiable convex and bounded functional such that ((partial f)^{-1}0neemptyset).

where is a bounded function such that (3.4).

Since as, there exists a bounded linear functional such that and.

Let be a functional such that and.

Let be a bilinear functional such that separates points in.

Let X be a real Banach space, and let Φ, Ψ : X → R be two continuously Gâteaux differentiable functionals such that Φ is bounded from below.

Let X be a real Banach space, (Phi, Psi:XtoBbb {R}) be two continuously Gâteaux differentiable functionals such that Φ is bounded from below and (Phi(0)=Psi(0)=0).

then are two continuous nonnegative functionals such that.

A Banach limit is a bounded linear functional on such that and for all bounded sequences in.

then there exists a uniformly bounded random variable such that.

Then for each there exist bounded operators with bounded inverses and, such that.