Some operator Bellman type inequalities

Bakherad, Mojtaba; Morassaei, Ali

doi:10.1016/j.indag.2015.04.006

Cited by 3 publications

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“…Popoviciu [22] extended Aczél's inequality for p ≥ 1. During the last decades, several generalizations, refinements, and applications of the Bellman inequality in various settings have been given and some results related to integral inequalities are presented, see [1,3,5,6,7,8,12,15,18,19,20,25].…”

Section: Introductionmentioning

confidence: 99%

Extensions of the operator Bellman and operator Holder type inequalities

Bakherad,

Kıttaneh

2024

Constructive Mathematical Analysis

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In this paper, we employ the concept of operator means as well as some operator techniques to establish new operator Bellman and operator H\"{o}lder type inequalities. Among other results, it is shown that if $\mathbf{A}=(A_t)_{t\in \Omega}$ and $\mathbf{B}=(B_t)_{t\in \Omega}$ are continuous fields of positive invertible operators in a unital $C^*$-algebra ${\mathscr A}$ such that $\int_{\Omega}A_t\,d\mu(t)\leq I_{\mathscr A}$ and $\int_{\Omega}B_t\,d\mu(t)\leq I_{\mathscr A}$, and if $\omega_f$ is an arbitrary operator mean with the representing function $f$, then \begin{align*} \left(I_{\mathscr A}-\int_{\Omega}(A_t \omega_f B_t)\,d\mu(t)\right)^p \geq\left(I_{\mathscr A}-\int_{\Omega}A_t\,d\mu(t)\right) \omega_{f^p}\left(I_{\mathscr A}-\int_{\Omega}B_t\,d\mu(t)\right) \end{align*} for all $0 < p \leq 1$, which is an extension of the operator Bellman inequality.

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Section: Introductionmentioning

confidence: 99%

Extensions of the operator Bellman and operator Holder type inequalities

Bakherad,

Kıttaneh

2024

Constructive Mathematical Analysis

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“…For further information about the matrix power mean, Karcher mean, operator mean and their properties, we refer the readers to [4,5,[14][15][16] and references therein. It is well known that for two positive definite matrices A and B, if A ≥ B, then…”

Section: Introductionmentioning

confidence: 99%

Some matrix power and Karcher means inequalities involving positive linear maps

Hajmohamadi

Lashkaripour

Bakherad

2018

Filomat

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In this paper, we generalize some matrix inequalities involving the matrix power means and Karcher mean of positive definite matrices. Among other inequalities, it is shown that if A = (A1,...,An) is an n-tuple of positive definite matrices such that 0 < m ? Ai ? M (i = 1,...,n) for some scalars m < M and ? = (w1,...,wn) is a weight vector with wi ? 0 and ?n,i=1 wi=1, then ?p (?n,i=1 wiAi)? ?p?p(Pt(?,A)) and ?p (?n,i=1 wiAi) ? ?p?p(?(?,A)), where p > 0,? = max {(M+m)2/4Mm,(M+m)2/42p Mm}, ? is a positive unital linear map and t ? [-1,1]\{0}.

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Some Estimations for the Generalized Relative Operator Entropy

Nikoufar

2022

Bull. Malays. Math. Sci. Soc.

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Some operator Bellman type inequalities

Abstract: Abstract. In this paper, we employ the Mond-Pečarić method to establish some reverses of the operator Bellman inequality under certain conditions. In particular, we show δI K

Cited by 3 publications

References 9 publications

Extensions of the operator Bellman and operator Holder type inequalities

Extensions of the operator Bellman and operator Holder type inequalities

Some matrix power and Karcher means inequalities involving positive linear maps

Some Estimations for the Generalized Relative Operator Entropy

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