Arithmetic mean-geometric mean inequality
Several matrix trace inequalities on Hermitian and skew Hermitian matrices
... the arithmetic mean-geometric mean inequality for positive definite matri- ces, which was an open question proposed by Bellman in []; Neudecke used a different method in [] to show a ...
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An Inequality for Logarithmic Mapping and Applications for the Relative Entropy
... weighted arithmetic mean - geometric mean inequality, we point out an analytic inequal- ity for the logarithmic map and apply it for the Kullback-Leibler distance in Information ...
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A Refinement of Jensen's Inequality with Applications for f-Divergence Measures
... Jensen inequality for convex functions plays a crucial role in the Theory of Inequalities due to the fact that other inequalities such as that arithmetic mean- geometric mean ...
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A Concept of Synchronicity Associated with Convex Functions in Linear Spaces and Applications
... Jensen inequality for convex functions plays a crucial role in the Theory of Inequalities due to the fact that other inequalities such as that arithmetic mean- geometric mean ...
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Applications of Arithmetic Geometric Mean Inequality
... well-known arithmetic-geometric mean inequality for singular values, due to Bhatia and Kittaneh, is one of the most important singular value in- equalities for compact ...to ...
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Weighted arithmetic–geometric operator mean inequalities
... In this paper, motivated by the aforementioned discussion, we extend (1.4)–(1.7) to the weighted arithmetic–geometric mean. In order to prove our results, we show a new opera- tor weighted ...
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Generalized Irreducible α Matrices and Its Applications
... In this paper, we present a new class of matrices-generalized irreducible α -matrices, and prove that a generalized irreducible α -matrix is an H -matrix. Furthermore, using the generalized ...
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On Anderson–Taylor type inequalities for τ measurable operators
... quadratic inequality for real ...Anderson–Taylor inequality as well as a related trace ...well-known arithmetic-geometric mean inequality for singular val- ues due to Bhatia and ...
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The Proofs of Product Inequalities in Vector Spaces
... Inequalities are inevitable tools in the mathematical analysis as they provide bases for sound arguments. Due to the enormous applications of inequalities, most researchers are shifting to this line of research by ...
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On the Lawson–Lim means and Karcher mean for positive invertible operators
... the arithmetic–geometric mean inequality of n-operators via Kantorovich ...reverse inequality of the weighted arithmetic and geometric means due to Lawson and Lim of ...
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Sharp bounds for the arithmetic geometric mean
... holds for all a, b > with a = b. The first inequality of (.) was first proposed by Carlson and Vuorinen [], it was proved in the literature [–] by different methods. Vamana- murthy and Vuorinen [] (also ...
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Some results of Heron mean and Young’s inequalities
... Heron mean, a refinement inequality about the classical interpolation between arithmetic mean and geometric mean by Heron mean is obtained, which is also applicable to ...
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The Proofs of the Arithmetic-Geometric Mean Inequality Through Both the Product and Binomial Inequalities
... AGM inequality has received much atten- tion and has been applied in the areas of statistics and ...AGM inequality was first introduced by Lagrange (as cited in ...AGM inequality has used to ...
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A Refinement of Jensen's Discrete Inequality for Differentiable Convex Functions
... Analytic Inequality Theory is determined by the fact that many other fundamental results such as: the Arithmetic Mean – Geometric Mean – Harmonic Mean inequality, or the ...
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A generalization and an application of the arithmetic–geometric mean inequality for the Frobenius norm
... the arithmetic–geometric mean inequality for the Frobenius ...Kittaneh’s inequality which was presented in (Joci´c and Kittaneh in ...
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Extensions of interpolation between the arithmetic geometric mean inequality for matrices
... MSC: Primary 47A64; secondary 15A60 Keywords: arithmetic-geometric mean; unitarily invariant norm; Hilbert-Schmidt norm; Cauchy-Schwarz inequality.. the eigenvalues of the positive semid[r] ...
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Sub super stabilizability of certain bivariate means via mean convexity
... tinuous second derivative), we can give a direct proof of the previous lemma without re- firing to the general result of [] stated for general positively homogeneous functions. In fact, let m be symmetric homogeneous ...
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Sharp bounds for a special quasi arithmetic mean in terms of arithmetic and geometric means with two parameters
... quasi-arithmetic mean E(a, b) in terms of the arithmetic mean A(a, b) and geometric mean G(a, b) with two ...and geometric means bounds for E(a, b) and find new bounds for ...
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On a result of Cartwright and Field
... Throughout this section, we assume that r > s. We omit the discussions on the conditions for equality in each inequality, we shall prove as one checks easily that the desired condi- tions hold by going through ...
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Sharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means
... Correspondence: [email protected] 2 School of Mathematics and Computation Sciences, Hunan City University, Yiyang, 413000, China Full list of author information is available at the e[r] ...
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