• The Pure and Applied Mathematics
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• v.25 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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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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• v.41 no.6
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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.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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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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• v.8 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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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.

• 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.