• Korean Journal of Mathematics
• /
• v.31 no.2
• /
• pp.189-201
• /
• 2023

In this article, we establish Hilbert-type integral inequalities with the help of a non-homogeneous kernel of hyperbolic function with best constant factor. We also study the obtained inequalities's equivalent form. Additionaly, several specific Hilbert's type inequalities with constant factors in the term of the rational fraction expansion of higher order derivatives of cotangent and cosine functions are presented.

• Journal of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.207-224
• /
• 2003

Some weighted Ostrowski type integral inequalities for vector-valued functions in Hilbert spaces are given. Applications for quadrature rules with values in Hilbert spaces are also pointed out.

• Kyungpook Mathematical Journal
• /
• v.50 no.1
• /
• pp.131-152
• /
• 2010

In this paper, by introducing some parameters we establish an extension of Hardy-Hilbert's integral inequality and the corresponding inequality for series. As an application, the reverses, some particular results and their equivalent forms are considered.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.547-556
• /
• 2012

A new Hardy-Hilbert type integral inequality for double series with weights can be established by introducing a parameter ${\lambda}$ (with ${\lambda}>1-\frac{2}{pq}$) and a weight function of the form $x^{1-\frac{2}{r}}$ (with $r$ > 1). And the constant factors of new inequalities established are proved to be the best possible. In particular, for case $r$ = 2, a new Hilbert type inequality is obtained. As applications, an equivalent form is considered.

• Kyungpook Mathematical Journal
• /
• v.49 no.3
• /
• pp.521-532
• /
• 2009

In this paper, by introducing a homogenous kernel of -4-degree, we establish a new Hilbert-type integral inequality with multi-parameter and a best constant factor. As applications, the equivalent form, the reverse forms and some particular results are given correspondingly.

• Kyungpook Mathematical Journal
• /
• v.54 no.1
• /
• pp.1-9
• /
• 2014

We build new Hilbert-type integral inequalities in the whole plane with the non-homogeneous kernel involving some parameters and the best constant factors. We also consider their reverse.

• Journal of the Korean Mathematical Society
• /
• v.43 no.5
• /
• pp.911-929
• /
• 2006

A refinement of $Gr\ddot{u}ss$ type inequality for the Bochner integral of vector-valued functions in real or complex Hilbert spaces is given. Related results are obtained. Application for finite Fourier transforms of vector-valued functions and some particular inequalities are provided.

• Bulletin of the Korean Mathematical Society
• /
• v.30 no.2
• /
• pp.201-212
• /
• 1993

It is our purpose in this paper to first establish an inequality in real uniformly smooth Banach spaces with modulus of smoothness of power type q > 1 that generalizes a well known Hilbert space inequality. Using our inequality, we shall then extend the above result of Qihou [15] on the Ishikawa iteration process from Hilbert spaces to these much more general Banach spaces. Furthermore, we shall prove that the Mann iteration process converges strongly to the unique fixed point of a quasi-contractive map in this general setting. No compactness assumption on K is required in our theorems.

• Kyungpook Mathematical Journal
• /
• v.49 no.4
• /
• pp.623-630
• /
• 2009

This paper deals with some new generalizations of the Hardy-Hilbert type integral inequalities with some parameters. We also consider the equivalent inequalities and the reverse forms.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.4
• /
• pp.543-559
• /
• 2002

Some inequalities and approximations for the finite filbert transform by the use of Ostrowski type inequalities for absolutely continuous functions are given.