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Some companion inequalities to Jensen's inequality [PDF]
Mathematical Inequalities & Applications, 2000 The authors obtain some new companion inequalities to Jensen's inequality (discrete or integral). The main results are given in a very general and abstract setting, for convex functions defined on an open convex set of a normed linear space. The differentiable cases, as well as sharpness questions are also considered.
Matić, M., Pečarić, J.
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New estimates for generalized Shannon and Zipf-Mandelbrot entropies via convexity results
Results in Physics, 2020 Shannon and Zipf-Mandelbrot entropies have several applications in various fields such as ecology, statistics, physics and information theory etc. The aim of this article is to utilize some results of Jensen’s inequality for convex functions and to ...
Khurshid Ahmad +4 more
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Monotone trace functions of several variables
, 2005 We investigate monotone operator functions of several variables under a trace or a trace-like functional. In particular, we prove the inequality \tau(x_1... x_n)\le\tau(y_1...
Hansen, Frank
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Another Converse of Jensen's Inequality [PDF]
, 2009 We give the best possible global bounds for a form of discrete Jensen’s inequality.
Simic, Slavko
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The Hadamard Determinant Inequality - Extensions to Operators on a Hilbert Space
, 2017 A generalization of classical determinant inequalities like Hadamard's inequality and Fischer's inequality is studied. For a version of the inequalities originally proved by Arveson for positive operators in von Neumann algebras with a tracial state, we ...
Nayak, Soumyashant
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A Refinement of Jensen’s and Minkowski’s Inequalities via Superquadratic Functions
International Journal of Mathematics and Mathematical SciencesWe provide in this note a different refinement of Jensen’s inequality obtained via superquadratic functions. A refinement of Minkowski’s and Hölder’s inequalities is also established as an application of our refined Jensen’s inequality.
Anton Asare-Tuah, Edward Prempeh
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An operator inequality related to Jensen’s inequality [PDF]
Proceedings of the American Mathematical Society, 2001 Summary: For bounded non-negative operators \(A\) and \(B\), Furuta showed \[ 0\leq A \leq B \text{ implies } A^{\frac{r}{2}}B^sA^{\frac{r}{2}} \leq (A^{\frac{r}{2}}B^tA^{\frac{r}{2}})^{\frac{s+r}{t+r}}\quad (0\leq r, 0\leq s \leq t).
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Structural results on convexity relative to cost functions
, 2012 Mass transportation problems appear in various areas of mathematics, their solutions involving cost convex potentials. Fenchel duality also represents an important concept for a wide variety of optimization problems, both from the theoretical and the ...
A. Karakhanyan +13 more
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Jensen's Functionals on Time Scales
Journal of Function Spaces and Applications, 2012 We consider Jensen’s functionals on time scales and discuss its properties and applications. Further, we define weighted generalized and power means on time scales.
Matloob Anwar +3 more
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Thermodynamic Limit for Finite Dimensional Classical and Quantum Disordered Systems
, 2004 We provide a very simple proof for the existence of the thermodynamic limit for the quenched specific pressure for classical and quantum disordered systems on a $d$-dimensional lattice, including spin glasses.
CRISTIAN GIARDINÀ +5 more
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