Sentence examples for best constant with from inspiring English sources

Riesz even managed to find the best constant with this seemingly inefficient approach; for the full story see [69].

In particular, the precise asymptotics of the best constant, with respect to the small parameter describing the heterogeneous boundary condition, was derived.

9, but the term has also been used for the Hardy like inequality with best constant for (r^{-1}) in three dimensions (which we discuss in Sect.

Motivated by a question of Brezis and Vázquez, we consider an Improved Hardy Inequality with best constant b, that we formally write as: −Δ⩾(N−22 21∣x∣2+bV x).

Recently, Wang and Yang [15] gave a more accurate reverse half-discrete Hilbert-type inequality, and Yang [16] provided the following half-discrete Hilbert inequality with best constant factor: int_{0}^{infty}f(x)sum _{n=1}^{infty}frac{a_{n}}{x+n},dx< pi|f||a|.

By using the way of weight functions and the technique of real analysis, a new Hilbert-type integral inequality with the non-homogeneous kernel in the whole plane with the best constant factor is given.

Applying weight functions, a half-discrete Hilbert-type inequality with a general homogeneous kernel of degree (-lambdain mathbf{R}) with the best constant factor (k ( lambda_{1} ) ) is obtained as follows: int_{0}^{infty}f(x)sum_{n=1}^{infty}k_{lambda } x,n a_{n},dx< k(lambda _{1})|f|_{p,phi}|a|_{q,psi}, (11) which is an extension of (10) (cf. [34]).

with the best constant factor k λ1).

The obtained inequalities are with the best constant factor.

We give a new Hilbert's inequality with a best constant factor and some parameters.

In this paper, we introduce some new inequalities with a best constant factor.