Sentence examples for established an integral from inspiring English sources

Moreover, in [5] Tian established an integral type of generalized Aczél-Vasić-Pečarić inequality.

In 1935, Grüss established an integral inequality which gives an estimation for the integral of a product in terms of the product of integrals [17].

In 1935, Grüss established an integral inequality which provides an estimation for the integral of a product in terms of the product of integrals [13, 19].

We have established an integral expression of (u_{n}(c)), which provides a direct proof of Theorem 1 in [1] and tell us that Theorem 1 is a natural result.

Molecular identification of 14 of the 70 genes demonstrates that they include six previously known tracheal genes, each with a novel function revealed by clonal analysis, and two well-known growth suppressors that establish an integral role for cell growth control in branching morphogenesis.

Under the assumption [IU] (i.e., the associated heat kernel is intrinsically ultracontractive), we establish an integral representation theorem: any nonnegative solution is represented uniquely by an integral on (D×{0})∪(∂MD×[0,T)), where ∂MD is the Martin boundary of D for the associated elliptic operator.

Now, we establish an integral expression of (u_{n}(c)).

To establish an integral expression of (u_{n}(c)), we first recall the following result we obtained in [7].

In this note, we will establish an integral expression of (u_{n}(c)), which tells us that Theorem 1 is a natural result.

In this note, we establish an integral expression of (u_{n}(c)), which provides a direct proof of Theorem 1 in (Mortici and Jang in Filomat 7 1535-1539, 2015).

In this article, we will introduce a new notion 'α-preinvex function', establish an integral identity for such a kind of functions, and find some Hermite-Hadamard type integral inequalities for a function that the power of the absolute value of its first derivative is α-preinvex.