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Remarks on the matrix arithmetic–geometric mean inequality
This note offers some remarks on a norm version of the matrix arithmetic–geometric inequality.
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The Alexandrov–Fenchel inequality
To illustrate the strength of this inequality, we observe that it yields the 1st Minkowski inequality and the 2nd Minkowski inequality as particular...
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Robust exponential stabilization of delayed neural networks with external disturbance via extended reciprocally convex matrix inequality
The paper investigates the robust exponential stabilization of delayed neural networks (NNs) with parameter uncertainties and external disturbance....
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Notes on the arithmetic–geometric mean inequality
In this paper, we give a matrix version of an equivalent form of the classical arithmetic–geometric mean inequality for two positive scalars....
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A sharp Bernstein–type inequality and application to the Carleson embedding theorem with matrix weights
We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real...
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Complex Hanner’s inequality for many functions
We establish Hanner’s inequality for arbitrarily many functions in the setting where the Rademacher distribution is replaced with higher dimensional...
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The Carne-Varopoulos Inequality
N. Varopoulos discovered a remarkable upper bound for the n-step transition probabilities of a symmetric, nearest-neighbor random walk on a finitely...
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Understanding Badly and Well-Behaved Linear Matrix Inequalities Via Semi-infinite Optimization
In this paper, we use a linear semi-infinite optimization approach to study badly and well-behaved linear matrix inequalities. We utilize a result on...
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A Heintze–Karcher Type Inequality in Hyperbolic Space
In this paper, we prove a new Heintze–Karcher type inequality for shifted mean convex hypersurfaces in hyperbolic space. As applications, we prove an...
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Refined Kato inequality and applications to norm and numerical radius inequalities
In this paper, we present refinements of Kato’s inequality; then, we employ these refinements to obtain some norm and numerical radius inequalities....
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The Poincaré Inequality for 3D-Vector Fields and the Neumann Problem
For 3D-vector fields we obtain a family of integral inequalities that can be regarded as the Poincaré inequality within the framework of field...
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On Bernstein Inequality via Chebyshev Polynomial
Motivated by applications to the Carleson embedding theorem with matrix weights, Culiuc and Treil proved a Bernstein-type inequality for complex...
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Matrix Equations
This chapter concentrates on solving the matrix equation $$\textbf{A}\textbf{x} =...
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Harnack Inequality and the Relevant Theorems on Finsler Metric Measure Manifolds
In this paper, we carry out in-depth research centering around the Harnack inequality for positive solutions to nonlinear heat equation on Finsler...
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Matrix concentration inequalities and free probability
A central tool in the study of nonhomogeneous random matrices, the noncommutative Khintchine inequality, yields a nonasymptotic bound on the spectral...