• East Asian mathematical journal
• /
• v.23 no.1
• /
• pp.59-73
• /
• 2007

A new reverse of the generalised triangle inequality that complements the classical results of Diaz and Metcalf is obtained. Applications for inner product spaces and for complex numbers are provided.

• Kyungpook Mathematical Journal
• /
• v.47 no.3
• /
• pp.411-423
• /
• 2007

This paper deals with a reverse Hardy-Hilbert's inequality with a best constant factor by introducing two parameters ${\lambda}$ and ${\alpha}$. We also consider the equivalent form and the analogue integral inequalities. Some particular results are given.

• Kyungpook Mathematical Journal
• /
• v.48 no.1
• /
• pp.93-100
• /
• 2008

In this paper, by introducing some parameters and estimating the weight function, we give a new Hilbert-type integral inequality with a best constant factor. The equivalent inequality and the reverse forms are considered.

• Korean Journal of Mathematics
• /
• v.28 no.1
• /
• pp.9-15
• /
• 2020

In 2012, Sulaiman [7] proved integral inequalities concerning reverse of Holder's. In this paper two results are given. First one is further improvement of the reverse Hölder inequality. We note that many existing inequalities related to the Hölder inequality can be proved via obtained this inequality in here. The second is further generalization of Sulaiman's integral inequalities concerning reverses of Holder's [7].

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.1
• /
• pp.33-37
• /
• 2022

In this short note, we prove an open problem for the interval (-∞, ∞), related to a reverse trigonometric Masjed-Jamei inequality presented in [2] and establish a new inequality of a similar kind.

• Kyungpook Mathematical Journal
• /
• v.49 no.3
• /
• pp.493-506
• /
• 2009

By using the improved Euler-Maclaurin summation formula and estimating the weight coefficients in this paper, a new dual Hardy-Hilbert's inequality and its reverse form are obtained, which are all with two pairs of conjugate exponents (p, q); (r, s) and a independent parameter ${\lambda}$. In addition, some equivalent forms of the inequalities are considered. We also prove that the constant factors in the new inequalities are all the best possible. As a particular case of our results, we obtain the reverse form of a famous Hardy-Hilbert's inequality.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.4
• /
• pp.725-738
• /
• 2005

A reverse of the Cauchy-Bunyakovsky-Schwarz integral inequality for complex-valued functions and applications for the finite Fourier transform are given.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.279-292
• /
• 2006

A reverse of Bessel's inequality in 2-inner product spaces and companions of $Gr\ddot{u}ss$ inequality with applications for determinantal integral inequalities are given.

• Kyungpook Mathematical Journal
• /
• v.49 no.4
• /
• pp.731-742
• /
• 2009

In this paper, by introducing parameters ${\lambda}$, ${\alpha}$and two pairs of conjugate exponents (p, q), (r, s) and applying the improved Euler-Maclaurin's summation formula, we establish a reverse of the slightly sharper Hilbert-type inequality. As applications, the strengthened version and the equivalent form are given.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.837-849
• /
• 2015

For $p{\geq}1$, sharp isoperimetric inequalities for the $L_p$-sine transform of isotropic measures are established. The corresponding reverse inequalities are obtained in an asymptotically optimal form. As applications of our main results, we present volume inequalities for convex bodies which are in $L_p$ surface isotropic position.