• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권1호
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• pp.39-48
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• 2018

In this work, by applying the binomial expansion, some refinements of the Young and Heinz inequalities are proved. As an application, a determinant inequality for positive definite matrices is obtained. Also, some operator inequalities around the Young's inequality for semidefinite invertible matrices are proved.

• 충청수학회지
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• 제24권3호
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• pp.583-586
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• 2011

A fractional Gagliardo-Nirenberg inequality is established. A sharp fractional Sobolev inequality is discussed as a direct consequence.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1181-1191
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• 2023

This paper investigates Young inequalities for matrices, a problem closely linked to operator theory, mathematical physics, and the arithmetic-geometric mean inequality. By obtaining new inequalities for unitarily invariant norms, we aim to derive a fresh Young inequality specifically designed for matrices.To lay the foundation for our study, we provide an overview of basic notation related to matrices. Additionally, we review previous advancements made by researchers in the field, focusing on Young improvements.Building upon this existing knowledge, we present several new enhancements of the classical Young inequality for nonnegative real numbers. Furthermore, we establish a matrix version of these improvements, tailored to the specific characteristics of matrices. Through our research, we contribute to a deeper understanding of Young inequalities in the context of matrices.

• 대한수학회논문집
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• 제25권2호
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• pp.207-214
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• 2010

In this paper, a generalized variational inequality problem is considered. An iterative method is studied for approximating a solution of the generalized variational inequality problem. Strong convergence theorem are established in a real Hilbert space.

• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.1021-1026
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• 2001

In this paper, we give an improvement of Carleman’s inequality by using the strict monotonicity of the power mean of n distinct positive numbers.

• 충청수학회지
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• 제22권2호
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• pp.287-291
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• 2009

A comparison of constants is given to show that a better constant for the Sobolev trace inequality can be obtained from the conjectured extremal function.

• 충청수학회지
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• 제21권4호
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• pp.493-499
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• 2008

We construct a minimizing sequence for the Sobolev trace inequality which satises compactness in the concentration compactness property.

• 대한수학회보
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• 제39권3호
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• pp.377-388
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• 2002

In this paper, we obtain an extension of an analogue of Hilbert's inequality involving series of nonnegative terms. The integral analogies of the main results are also given.

• 충청수학회지
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• 제26권1호
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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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• 제48권2호
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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.