Results 61 to 70 of about 38,693 (157)
Norm inequalities for weighted power means of operators
Linear Algebra and its Applications, 2002 Let \(A_{i}\), \(X_{i}\) and \(Y_{i}\) be bounded linear operators on a Hilbert space for \(i=1,2,\dots ,n\). In the present paper, the authors prove the following norm inequalities: (i) If \(\sum_{i=1}^{n}X^{*}_{i}X_{i}\leq I\), \(\sum_{i=1}^{n}Y^{*}_{i}Y_{ i}\leq I\) and \(r\geq 1\), then \[ \Bigg|\Bigg|\Bigg|\Bigg |\sum_{i =1}^{n} X_{i}^{*}A_{i}Y_{i}
Hirzallah, Omar, Kittaneh, Fuad
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New Quantum Estimates of Trapezium-Type Inequalities for Generalized ϕ-Convex Functions
Mathematics, 2019 In this paper, a quantum trapezium-type inequality using a new class of function, the so-called generalized ϕ -convex function, is presented. A new quantum trapezium-type inequality for the product of two generalized ϕ -convex functions is ...
Miguel J. Vivas-Cortez +3 more
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Matrix power means and Pólya-Szegő type inequalities
Surveys in Mathematics and its Applications, 2020 Summary: It is shown that, if \(\mu\) is a compactly supported probability measure on \(\mathbb{M}^+_n\), then, for every unit vector \(\eta\in\mathbb{C}^n\), there exists at compactly supported probability measure (denoted by \(\langle\mu\eta,\eta\rangle)\) on \(\mathbb{R}^+\) so that the inequality \[\langle P_t(\mu)\eta,\eta\rangle\le P_t(\langle\mu
Mohsen Kian, Fatemeh Rashid
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Jessen's functional, its properties and applications
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2012 In this paper we consider Jessen's functional, defined by means of a positive isotonic linear functional, and investigate its properties. Derived results are then applied to weighted generalized power means, which yields extensions of some recent results,
Lovričević Neda +2 more
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Scaled evolution of the reversed power mean inequalities
FilomatMotivated by the Hanin inequality, in this paper we study a class of reversed power mean inequalities that does not depend on a weight function. We first give the reverse of the basic power mean inequality describing the monotonic behavior of means. Then, we establish the scaled, i.e. two-parametric versions of the obtained inequalities. By scaling, we
Marija Bosnjak +2 more
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Power mean inequality of generalized trigonometric functions
, 2012 9
Bhayo, Barkat Ali, Vuorinen, Matti
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Complementary inequalities to Davis-Choi-Jensen's inequality and operator power means
, 2021 Let $f$ be an operator convex function on $(0,\infty)$, and $Φ$ be a unital positive linear maps on $B(H)$. we give a complementary inequality to Davis-Choi-Jensen's inequality as follows \begin{equation*} f(Φ(A))\geq \frac{4R(A,B)}{(1+R(A,B))^2}Φ(f(A)), \end{equation*} where $R(A, B)=\max\{r(A^{-1}B) ,r(B^{-1}A)\}$ and $r(A)$ is the spectral radius of
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Estimations of the weighted power mean by the Heron mean and related inequalities for determinants and traces [PDF]
Mathematical Inequalities & Applications, 2019 Summary: For positive real numbers \(a\) and \(b\), the weighted power mean \(P_{t,q}(a,b)\) and the weighted Heron mean \(K_{t,q}(a,b)\) are defined as follows: For \(t\in [0,1]\) and \(q\in \mathbb R\), \(P_{t,q}(a,b) = \{(1 - t)a^q+tb^q\}^{\frac1q}\) and \(K_{t,q}(a,b) = (1 -q)a^{1-t}b^t+ q\{(1 -t)a +tb\}\). These means generalize the arithmetic and
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Some inequalities for weighted power mean
Journal of Mathematical InequalitieszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Mathematical and Computer Modelling of Dynamical SystemsFractional calculus is extremely important and should not be undervalued due to its critical role in the theory of inequalities. In this article, different generalized Hermite-Hadamard type inequalities for functions whose modulus of first derivatives ...
Asfand Fahad +5 more
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