Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 16

... on the operator inequalities involving improved Y oung’ s and its reverse inequalities relating to the Kantorovich constant Jie Zhang * and Junliang Wu * Correspondence...

Kantorovich constant | operator inequality | Mathematics | 15A15 | 47A30 | 15A42 | Analysis | Young’s inequality | Mathematics, general | progress | Applications of Mathematics | 15A60 | Kittaneh-Manasrah inequality | MATHEMATICS | MATHEMATICS, APPLIED | MATRICES | Young's inequality | Scalars | Operators | Promotion | Inequalities | Research

Kantorovich constant | operator inequality | Mathematics | 15A15 | 47A30 | 15A42 | Analysis | Young’s inequality | Mathematics, general | progress | Applications of Mathematics | 15A60 | Kittaneh-Manasrah inequality | MATHEMATICS | MATHEMATICS, APPLIED | MATRICES | Young's inequality | Scalars | Operators | Promotion | Inequalities | Research

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 2016, Volume 10, Issue 2, pp. 559 - 570

In this article, we study the further refinements and reverses of the Young and Heinz inequalities with the Kantorovich constant...

Heinz mean | Kantorovich constant | Operator inequalities | Young inequality | MATHEMATICS | MATHEMATICS, APPLIED | operator inequalities | REVERSE INEQUALITIES | HILBERT-SPACE

Heinz mean | Kantorovich constant | Operator inequalities | Young inequality | MATHEMATICS | MATHEMATICS, APPLIED | operator inequalities | REVERSE INEQUALITIES | HILBERT-SPACE

Journal Article

3.
Full Text
Reverses of Young Type Inequalities for Matrices Using the Classical Kantorovich Constant

Results in Mathematics, ISSN 1422-6383, 3/2019, Volume 74, Issue 1, pp. 1 - 10

...) applying the Kantorovich constant. As an application of these numerical versions, we study some matrix inequalities for the Hilbert...

reverse Young type inequality | Hilbert–Schmidt norm | 15A45 | Mathematics, general | matrix inequalities | Mathematics | classical Kantorovich constant | 15A60 | 47A30 | MATHEMATICS | MATHEMATICS, APPLIED | Hilbert-Schmidt norm | HEINZ INEQUALITIES

reverse Young type inequality | Hilbert–Schmidt norm | 15A45 | Mathematics, general | matrix inequalities | Mathematics | classical Kantorovich constant | 15A60 | 47A30 | MATHEMATICS | MATHEMATICS, APPLIED | Hilbert-Schmidt norm | HEINZ INEQUALITIES

Journal Article

Numerical Algorithms, ISSN 1017-1398, 6/2011, Volume 57, Issue 2, pp. 235 - 253

... (Adv Nonlinear Var Inequal 8:93–99, 2005, 2007) to hold for systems of equations with constant rank derivatives...

Numeric Computing | Gauss–Newton method | Theory of Computation | Recurrent functions | Banach space | Newton–Kantorovich hypothesis | Algorithms | Algebra | Computer Science | Mathematics, general | 65H10 | 65G99 | 49M15 | 65J15 | 47H17 | Majorizing sequences | Newton-Kantorovich hypothesis | Gauss-Newton method | NEWTON-LIKE METHODS | MATHEMATICS, APPLIED | OPERATOR-EQUATIONS | THEOREM | COMPLEXITY | CONVERGENCE | Derivatives (Financial instruments) | Rankings | Nonlinear equations | Mathematical analysis | Newton methods | Constants | Mathematical models | Derivatives | Clarity | Convergence

Numeric Computing | Gauss–Newton method | Theory of Computation | Recurrent functions | Banach space | Newton–Kantorovich hypothesis | Algorithms | Algebra | Computer Science | Mathematics, general | 65H10 | 65G99 | 49M15 | 65J15 | 47H17 | Majorizing sequences | Newton-Kantorovich hypothesis | Gauss-Newton method | NEWTON-LIKE METHODS | MATHEMATICS, APPLIED | OPERATOR-EQUATIONS | THEOREM | COMPLEXITY | CONVERGENCE | Derivatives (Financial instruments) | Rankings | Nonlinear equations | Mathematical analysis | Newton methods | Constants | Mathematical models | Derivatives | Clarity | Convergence

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 2011, Volume 5, Issue 4, pp. 551 - 556

The Specht ratio S(h) is the optimal constant in the reverse of the arithmetic-geometric mean inequality, i.e., if 0 < m <= a, b <= M and h = M/m, then (1 - mu)a + mu b <= S(h)a(1-mu) b(mu...

Operator inequality | Specht ratio | Operator means | Kantorovich constant | Young inequality | Arithmetic-geometric-harmonic mean inequality | MATHEMATICS | MATHEMATICS, APPLIED | operator inequality | operator means | arithmetic-geometric-harmonic mean inequality

Operator inequality | Specht ratio | Operator means | Kantorovich constant | Young inequality | Arithmetic-geometric-harmonic mean inequality | MATHEMATICS | MATHEMATICS, APPLIED | operator inequality | operator means | arithmetic-geometric-harmonic mean inequality

Journal Article

International Journal of Structural Stability and Dynamics, ISSN 0219-4554, 06/2007, Volume 7, Issue 2, pp. 179 - 192

This work presents highly accurate numerical calculations of the buckling loads for thin elastic rectangular plates with known constant in-plane stresses, and in- plane shear loading that is increased...

Exact element method | Extended Kantorovich method | Stability | Shear buckling | Thin plates | ENGINEERING, CIVIL | MECHANICS | extended Kantorovich method | thin plates | stability | shear buckling | LOADS | ENGINEERING, MECHANICAL | exact element method

Exact element method | Extended Kantorovich method | Stability | Shear buckling | Thin plates | ENGINEERING, CIVIL | MECHANICS | extended Kantorovich method | thin plates | stability | shear buckling | LOADS | ENGINEERING, MECHANICAL | exact element method

Journal Article

Issues of analysis, ISSN 2306-3432, 02/2020, Volume 27, Issue 1, pp. 38 - 51

A hyperbolic formulation has been established for the generalized Kantorovich constant...

hyperbolic formulation for kantorovich constant | generalized kantorovich constant | a dual generalized kantorovich constant | hyperbolic inequalities

hyperbolic formulation for kantorovich constant | generalized kantorovich constant | a dual generalized kantorovich constant | hyperbolic inequalities

Journal Article

8.
Full Text
NEW VERSIONS OF REVERSE YOUNG AND HEINZ MEAN INEQUALITIES WITH THE KANTOROVICH CONSTANT

Taiwanese journal of mathematics, ISSN 1027-5487, 4/2015, Volume 19, Issue 2, pp. 467 - 479

We show new versions of reverse Young inequalities by virtue of the Kantorovich constant, and utilizing the new reverse Young inequalities we give the reverses of the weighted arithmetic-geometric...

Mathematical constants | Mathematical inequalities | Reverse Young inequalities | Kantorovich constant | Operators | Unitarily invariant norms | MATHEMATICS

Mathematical constants | Mathematical inequalities | Reverse Young inequalities | Kantorovich constant | Operators | Unitarily invariant norms | MATHEMATICS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2006, Volume 412, Issue 2, pp. 526 - 537

...) via generalized Kantorovich constant K( p). As some applications of two reverse inequalities, we shall show two trace reverse inequalities involving −Tr[ T p ( A∣ B)] and D p ( A∥ B...

Generalized Kantorovich constant | Tsallis relative operator entropy | Specht ratio | Relative operator entropy | Tsallis relative entropy | Umegaki relative entropy | MATHEMATICS, APPLIED | relative operator entropy | generalized Kantorovich constant

Generalized Kantorovich constant | Tsallis relative operator entropy | Specht ratio | Relative operator entropy | Tsallis relative entropy | Umegaki relative entropy | MATHEMATICS, APPLIED | relative operator entropy | generalized Kantorovich constant

Journal Article

Linear & multilinear algebra, ISSN 1563-5139, 2018, Volume 67, Issue 11, pp. 2253 - 2281

... Kantorovich constant.

Ando-Hiai inequality | generalized Kantorovich constant | Karcher mean | power mean | geometric mean | Operator mean | Ando–Hiai inequality | MATRIX POWER | MATHEMATICS | Inequalities

Ando-Hiai inequality | generalized Kantorovich constant | Karcher mean | power mean | geometric mean | Operator mean | Ando–Hiai inequality | MATRIX POWER | MATHEMATICS | Inequalities

Journal Article

Aequationes mathematicae, ISSN 1420-8903, 2017, Volume 92, Issue 1, pp. 25 - 37

In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen type and Jensen–Mercer type inequalities....

Secondary 46L05 | Strongly convex functions | Jensen’s inequality | Primary 47A63 | Analysis | Operator inequality | Mathematics | 26B25 | Combinatorics | MATHEMATICS | MATHEMATICS, APPLIED | Jensen's inequality | YOUNG | BOUNDS | KANTOROVICH CONSTANT | Mathematics - Functional Analysis

Secondary 46L05 | Strongly convex functions | Jensen’s inequality | Primary 47A63 | Analysis | Operator inequality | Mathematics | 26B25 | Combinatorics | MATHEMATICS | MATHEMATICS, APPLIED | Jensen's inequality | YOUNG | BOUNDS | KANTOROVICH CONSTANT | Mathematics - Functional Analysis

Journal Article

Houston journal of mathematics, ISSN 0362-1588, 2019, Volume 45, Issue 3, pp. 815 - 830

... <= v <= 1, p >= 2, r = min{v, 1 - v}, h = M/m, h' = M'/m', K(h) = (1+h)(2)/4h and r(1) = min{2r, 1 - 2r}. We also obtain a reverse of the Ando inequality for positive linear maps via the Kantorovich constant.

MATHEMATICS | Kantorovich's constant | positive linear map | Ando's inequality | Operator mean

MATHEMATICS | Kantorovich's constant | positive linear map | Ando's inequality | Operator mean

Journal Article

Studia Scientiarum Mathematicarum Hungarica, ISSN 0081-6906, 09/2018, Volume 55, Issue 3, pp. 363 - 373

...] via Kantorovich constant. Then we apply these inequalities to establish corresponding inequalities for the Hilbert-Schmidt norm and the trace norm.

Reverse classical Young inequality | Refinement | Kantorovich constant | Hilbert- Schmidt norm | Positive definite matrices | MATHEMATICS | OPERATOR INEQUALITIES | MEAN INEQUALITIES

Reverse classical Young inequality | Refinement | Kantorovich constant | Hilbert- Schmidt norm | Positive definite matrices | MATHEMATICS | OPERATOR INEQUALITIES | MEAN INEQUALITIES

Journal Article

Mathematica Slovaca, ISSN 1337-2211, 2019, Volume 69, Issue 4, pp. 919 - 930

We obtain a refined Young type inequality in this paper. The conclusion is presented as follows: Let , ∈ (𝓗) be two positive operators and ∈ [0, 1], then...

Secondary 46B20 | Kantorovich constant | positive linear map | Primary 47A63 | Young inequality | arithmetic-geometric means | REVERSE YOUNG | MATHEMATICS | OPERATOR INEQUALITIES | Arrays | Inequality

Secondary 46B20 | Kantorovich constant | positive linear map | Primary 47A63 | Young inequality | arithmetic-geometric means | REVERSE YOUNG | MATHEMATICS | OPERATOR INEQUALITIES | Arrays | Inequality

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 9

...; Lawson–Lim geometric mean; Ando–Li–Mathias geometric mean; Kantorovich constant 1 Introduction Let B(H)b et h eC ∗ -algebra of all bounded linear operators...

Lawson–Lim geometric mean | Kantorovich constant | 15A45 | Analysis | Ando–Li–Mathias geometric mean | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | Karcher mean | 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | Ando-Li-Mathias geometric mean | KANTOROVICH INEQUALITY | Lawson-Lim geometric mean | Operators | Research

Lawson–Lim geometric mean | Kantorovich constant | 15A45 | Analysis | Ando–Li–Mathias geometric mean | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | Karcher mean | 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | Ando-Li-Mathias geometric mean | KANTOROVICH INEQUALITY | Lawson-Lim geometric mean | Operators | Research

Journal Article

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, ISSN 1735-8515, 10/2017, Volume 43, Issue 5, pp. 1301 - 1311

Some improvements of Young inequality and its reverse for positive numbers with Kantorovich constant K(t, 2) = (1+t)(2) /4t are given...

REVERSE YOUNG | MATHEMATICS | Kantorovich constant | Young inequality | MATRICES | Heinz mean | POSITIVE OPERATORS | Hilbert-Schmidt norm | HEINZ INEQUALITIES

REVERSE YOUNG | MATHEMATICS | Kantorovich constant | Young inequality | MATRICES | Heinz mean | POSITIVE OPERATORS | Hilbert-Schmidt norm | HEINZ INEQUALITIES

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 08/2018, Volume 68, Issue 4, pp. 803 - 810

... and their reverses, using two inequalities where = min{ , 1 – }, = max{ ,1 – } and ,2) = is the Kantorovich constant, and where = max and ) = exp (4 (1 – )( ,2)–1...

Kantorovich constant | Secondary 47A64 | Primary 47A63 | Young inequality | 47B65 | Heinz mean | weighted arithmetic and geometric mean | strictly positive operator | MATHEMATICS | MATRICES

Kantorovich constant | Secondary 47A64 | Primary 47A63 | Young inequality | 47B65 | Heinz mean | weighted arithmetic and geometric mean | strictly positive operator | MATHEMATICS | MATRICES

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 2016, Volume 10, Issue 3, pp. 713 - 723

In this paper, we obtain some improved Young and Heinz inequalities and the reverse versions for scalars and matrices with Kantorovich constant, equipped with the 1 Hilbert-Schmidt norm, and then we...

Kantorovich constant | Hilbert-Schmidt norm | Young's inequality | Positive semi-definite matrix | MATHEMATICS | MATHEMATICS, APPLIED

Kantorovich constant | Hilbert-Schmidt norm | Young's inequality | Positive semi-definite matrix | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 03/2015, Volume 63, Issue 3, pp. 636 - 649

.... Among others, we show complements of the -variable Ando-Hiai inequality for the Ando-Li-Mathias geometric mean by means of the Kantorovich constant.

unitarily invariant norm | Specht ratio | matrix geometric mean | Kantorovich constant | Ando-Li-Mathias geometric mean | Ando-Hiai inequality | Karcher mean | chaotic geometric mean | Ando–Li–Mathias geometric mean | Ando–Hiai inequality | INEQUALITIES | 47A64 | 47A30 | 47A63 | MATHEMATICS | Inequality | Constants | Complement | Algebra | Chaos theory | Inequalities | Images

unitarily invariant norm | Specht ratio | matrix geometric mean | Kantorovich constant | Ando-Li-Mathias geometric mean | Ando-Hiai inequality | Karcher mean | chaotic geometric mean | Ando–Li–Mathias geometric mean | Ando–Hiai inequality | INEQUALITIES | 47A64 | 47A30 | 47A63 | MATHEMATICS | Inequality | Constants | Complement | Algebra | Chaos theory | Inequalities | Images

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 8

.... Concretely, we obtain refined Young inequalities with the Kantorovich constant, the reverse ratio type and difference type inequalities for arithmetic-geometric operator...

Kantorovich constant | Analysis | Young inequality | arithmetic-geometric means | Mathematics, general | Mathematics | Applications of Mathematics | operator iteration | 47A30 | 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | HILBERT-SPACE | Concretes | Operators | Inequalities

Kantorovich constant | Analysis | Young inequality | arithmetic-geometric means | Mathematics, general | Mathematics | Applications of Mathematics | operator iteration | 47A30 | 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | HILBERT-SPACE | Concretes | Operators | Inequalities

Journal Article

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