• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.281-288
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• 2010

By introducing some parameters and using the way of weight function and the technic of real analysis and complex analysis, a new Hilbert-type integral inequality with a best constant factor and a combination kernel involving two mean values is given, which is an extension of Hilbert's integral inequality. As applications, the equivalent form and the reverse forms are considered.

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

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

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

• Structural Engineering and Mechanics
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• v.23 no.4
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• pp.431-447
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• 2006

A new incremental finite element model is developed to simulate the frictional contact of elastic bodies. The incremental convex programming method is exploited, in the framework of finite element approach, to recast the variational inequality principle of contact problem in a discretized form. The non-classical friction model of Oden and Pires is adopted, however, the friction effect is represented by an equivalent non-linear stiffness rather than additional constraints. Different parametric studies are worked out to address the versatility of the proposed model.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.7-10
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• 2009

With the introduction of a new parameter $n{\geq}1$, Kim generalized an upper bound for the exponential function that implies the inequality between the arithmetic and geometric means. By a change of variable, this generalization is equivalent to exp $(\frac{n(x-1)}{n+x-1})\;\leq\;\frac{n-1+x^n}{n}$ for real ${n}\;{\geq}\;1$ and x > 0. In this paper, we show that this inequality is true for real x > 1 - n provided that n is an even integer.

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.189-201
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• 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 Information Processing Systems
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• v.13 no.2
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• pp.417-427
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• 2017

Power allocation is an important factor for cognitive radio networks to achieve higher communication capacity and faster equilibrium. This paper considers power allocation problem to each cognitive user to maximize capacity of the cognitive systems subject to the constraints on the total power of each cognitive user and the interference levels of the primary user. Since this power control problem can be formulated as a mixed-integer nonlinear programming (NP) equivalent to variational inequality (VI) problem in convex polyhedron which can be transformed into complementary problem (CP), we utilize modified projection method to solve this CP problem instead of finding NP solution and give a power control allocation algorithm with a subcarrier allocation scheme. Simulation results show that the proposed algorithm performs well and effectively reduces the system power consumption with almost maximum capacity while achieve Nash equilibrium.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.381-396
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• 2018

In this paper we have considered a system of mixed generalized variational inequality problems defined on two different domains in a Hilbert space. It has been shown that the solution of a system of mixed generalized variational inequality problems is equivalent to altering point formulation of some mappings. A new parallel S-iteration type process has been considered which converges strongly to the solution of a system of mixed generalized variational inequality problems.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.4
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• pp.613-624
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• 2021

This paper analyzes the relationship between income distribution and energy consumption from a Pareto optimal approach. For this purpose, the causality relationship between electricity consumption per capita (kWh) with respect to country groups and energy consumption per capita (kg of oil equivalent) along with gross domestic product per capita was analyzed. In addition to this purpose, a Pareto analysis was conducted to determine the countries with the highest per capita national income, how much of the world total energy they consume, and whether the law of power in the energy and electricity markets exists. Finally, the impact of official development assistance provided to low-income countries by high-income countries on the low-income countries' electricity and energy consumption was analyzed. In other words, it was questioned whether pareto redistribution policies serve the purpose or not. The Engle-Granger causality approach was used in the analysis of the causality relationship between variables. Our analysis indicated that, first, the energy data of the country groups may be inadequate in revealing income inequalities. Second, the existence of Pareto law of power and global income inequality can be explained based on energy data. Finally, Pareto optimal redistribution policies to eliminate income inequality remain inadequate in practice.