Sentence examples similar to in its integral version from inspiring English sources

In recent years several authors have given considerable attention to Hilbert's double-series inequality together with its integral version, inverse version, and various generalizations (see [1 9]).

We may state its integral version as follows: Let (x,y:[alpha,beta]rightarrow [ a,b]) be two functions and (w:[alpha,beta]rightarrow mathbb{R} ) continuous function.

We stayed in its integral hotel, where Modernism is almost cosy, with parquet, plate-glass and black leather couches.

This summary version is based on an integral version that was validated and published in 2000 (Desport et al, 2000) and is also available at: http://www.fnclcc.fr.

We will present in this paper the integral version of inequalities (3) and (4).

In Section 2, we present an integral version of some results recently proved in [1].

In this paper, we use an integral version of Leray-Schauder degree theory under Katriel's frame to prove the existence of periodic solutions for our SIR model.

In 2002, Branciari [8] gave an integral version of the Banach contraction principles and showed the following fixed point theorem.

The integral version refers to the given interval and its subinterval sharing the common barycenter.

and is an integral version of (1.11).

An integral version utilizes a measure.