In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.

It is well known that an integral domain D is a UFD if and only if every nonzero prime ideal of D contains a nonzero principal prime. This is the so-called Kaplansky’s theorem. In this paper, we give this type of characterizations of a graded PvMD (resp., G-GCD domain, GCD domain, Bézout domain, valuation domain, Krull domain, π-domain).

In 2012, W. T. Sulaiman presented new kinds of Hardy’s integral inequalities. In this paper, we derive some new extensions of the famous Hardy’s integral inequality. The results present direct generalization of the original Hardy inequality. In addition, the corresponding reverse relation is also obtained.

A nonlinear stochastic integral equation of the Hammerstein type in the form x(t; c) = h(t; co) + f k(t, s; co)f (s, x(s; co)) dy (s) is studied where t E S, a v-finite measure space with certain properties, co E Q, the supporting set of a probability measure space (Q, A, P), and the integral is a Bochner integral. A random solution of the equation is defined to be a second order vector-valued ...

By estimating a weight function, a reverse Hardy-Hilbert-type integral inequality with a best constant factor is obtained. As an application, some equivalent forms and some particular results have been established.

Most standard fractal image compression techniques rely on using an IFS operator directly on the image function. Sometimes, however , it is more convenient to work on a faithful representation of the image which, in certain applications, may be a transformed version of the image. For example, if an MRI image is scanned in as frequency data it may be more natural to work on the Fourier transform...

In this paper we prove some new results concerning multi-dimensional Hardy type integral inequalities and also some corresponding limit Pólya–Knopp type inequalities.