• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.163-174
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• 1991

This is a continuation of the author's previous work [17]. In this paper, we consider mainly variational inequalities for single-valued functions. We first obtain a generalization of the variational type inequality of Juberg and Karamardian [10] and apply it to obtain strengthened versions of the Hartman-Stampacchia inequality and the Brouwer fixed point theorem. Next, we obtain fairly general versions of Browder's variational inequality [5] and its subsequent generalizations due to Brezis et al [4], Takahashk [23], Shih and Tan [19], Simons [20], and others. Finally, in this paper, we obtain a variational inequality for non-real locally convex t.v.s. which generalizes a result of Shih and Tan [19].

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.281-288
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• 2012

In this paper, the author defines a new generalized ${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.105-110
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• 2013

A logarithmic composition inequality in Besov spaces is derived which generalizes Vishik's inequality: ${\parallel}f{\circ}g{\parallel}_{B^s_{p,1}}{\leq}(1+{\log}({\parallel}{\nabla}g{\parallel}_{L^{\infty}}{\parallel}{\nabla}g^{-1}{\parallel}_{L^{\infty}})){\parallel}f{\parallel}_{B^s_{p,1}}$, where $g$ is a volume-preserving diffeomorphism on ${\mathbb{R}}^n$.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.207-222
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• 2008

A new counterpart of Bessel's inequality for orthonormal families in real or complex 2-inner product spaces is obtained. Applications for some Gr$\"{u}$ss inequality for determinantal integral inequalities are also provided.

• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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• pp.191-200
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• 2024

Motivated by the previously reported results, this work attempts to provide fresh refinements to both vector and numerical radius inequalities by providing a refinement to the well known Buzano's inequality which as a consequence yielded another refinement of the Cauchy-Schwartz (CS) inequality. Utilizing the new refinements of the Buzano's and Cauchy-Schwartz inequalities, we proceed to obtain various vector and numerical radius type inequalities. Methods used in the paper are standard for the operator theory inequality topics.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.441-452
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• 2021

In this paper, improved power-mean integral inequality, which provides a better approach than power-mean integral inequality, is proved. Using Hölder-İşcan integral inequality and improved power-mean integral inequality, some inequalities of Hadamard's type for functions whose derivatives in absolute value at certain power are quasi-convex are given. In addition, the results obtained are compared with the previous ones. Then, it is shown that the results obtained together with identity are better than those previously obtained.

• East Asian mathematical journal
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• v.29 no.5
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• pp.537-543
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• 2013

Recent results of Wu and Tian on refined H$\ddot{o}$lder's inequality for two sequences are extended to the case of three sequences.

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

• Asian Journal for Public Opinion Research
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• v.6 no.1
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• pp.1-17
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• 2018

As societal interest in inequality increases in Korea, both public and academic discussion on inequality is also on the rise. In order to more effectively discuss the problems of rising inequality, however, it is essential to study the consequences and implications of inequality. This study examines one of the consequences of inequality, particularly on individuals - the relationship between an individual's perception of inequality and his/her evaluation of societal health, such as social trust and social mobility. According to a statistical analysis of the Korean Academic Multimode Open Survey for Social Sciences (KAMOS), those who perceive the level of income and wealth inequality in Korea as more unequal tend to have a lower level of trust toward Korean society and Korean people, as well as a lower expectation for both intra- and intergenerational social mobility. This study, which shows that rising inequality could have a negative impact at the individual level, not only extends the scope of the consequence-of-inequality studies from the society-oriented toward the individual-oriented, but it also has significant implications for the field, suggesting a new direction for future studies.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.115-120
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• 1990

We obtain one simple generalization of the Gronwall's inequality by using the Viswanatham's theorem.