• 제목/요약/키워드: young inequality

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SOME OPERATOR INEQUALITIES INVOLVING IMPROVED YOUNG AND HEINZ INEQUALITIES

  • Moazzen, Alireza
    • 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.

STUDY OF YOUNG INEQUALITIES FOR MATRICES

  • M. AL-HAWARI;W. GHARAIBEH
    • 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.

ON CARLEMAN'S INEQUALITY AND ITS IMPROVEMENT

  • Kim, Young-Ho
    • 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.

LOGARITHMIC COMPOSITION INEQUALITY IN BESOV SPACES

  • Park, Young Ja
    • 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 ${\mathbb{R}}^n$.

On Bessel's and Grüss Inequalities for Orthonormal Families in 2-Inner Product Spaces and Applications

  • Dragomir, Sever Silverstru;Cho, Yeol-Je;Kim, Seong-Sik;Kim, Young-Ho
    • 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.