Sentence examples for by a classical result from inspiring English sources

By a classical result of Minty [17], the proximal subproblem always has an exact solution, which is unique.

Hence, by a classical result (see [11]), there is a (unique) extension G : D ′ ¯ → ℝ n of f which is harmonic in D'.

Also, by a classical result of Kœnigs there is an analytic mapσsuch thatσ∘φ=λσ(λ=φ′(0)≠0), which is one-to-one whenφis one-to-one.

For example, if X is uniformly convex and (g:[0,+infty)rightarrow mathbb{R}) is a continuous, strictly increasing function, then, by a classical result, the functional (urightarrow g(|u|)) belongs to the class (Gamma_{X}). ([32], Theorem 2).

If X is uniformly convex and (g:[0,+infty )rightarrow mathbb{R}) is a continuous and strictly increasing function, then, by a classical result, the functional (urightarrow g Vert u Vert )) belongs to the class (mathcal{W}_{X}). [43].

By using a classical result of Coifman et al. (see [1]), we know that the commutator [ b, T ] is bounded on L p ( R n ) ( 1 < p < ∞ ).

The first proof (unpublished), offered by Warren Dicks, utilized a classical result of Cartan and Eilenberg [53, Theorem X1.3.1], which yields that the flat dimension of a tensor product is at least the sum of the flat dimensions of the two algebras.

We provide a new proof of a classical result by Bressan on the Cauchy problem for first-order differential inclusions with null initial condition.

The proof exploits a simplification of a classical result by Rogers (1993) which characterizes the attainable joint laws for the supremum and the drawdown of a uniformly integrable martingale (not necessarily continuous), combined with classical convex duality results from Rockefellar (1974) using paired spaces with compatible locally convex topologies and the Hahn Banach theorem.

The Nielsen number is of particular interest since a classical result by Wecken [1] states that the Nielsen number coincides with the minimal number of fixed point in the homotopy class of the map when the dimension of M is at least three.

We will also call begin{aligned} M_{m, Lambda }text { the set of symmetric } mtimes m text { real valued matrix, satisfying } (5.2) end{aligned} (5.3 If A is the identity matrix then the existence of a heat kernel for the operator (L_A) is a by now classical result due to Folland [37] and Rothschild and Stein [76].