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دسترسی آزاد مقاله
1 - Some improvements of numerical radius inequalities via Specht’s ratio
Y. Khatib M. HassaniWe obtain some inequalities related to the powers of numericalradius inequalities of Hilbert space operators. Some results thatemploy the Hermite-Hadamard inequality for vectors in normed linearspaces are also obtained. We improve and generalize someinequalities with re چکیده کاملWe obtain some inequalities related to the powers of numericalradius inequalities of Hilbert space operators. Some results thatemploy the Hermite-Hadamard inequality for vectors in normed linearspaces are also obtained. We improve and generalize someinequalities with respect to Specht's ratio. Among them, we showthat, if $A, B\in \mathcal{B(\mathcal{H})}$ satisfy in someconditions, it follows that \begin{equation*} \omega^2(A^*B)\leq \frac{1}{2S(\sqrt{h})}\Big\||A|^{4}+|B|^{4}\Big\|-\displaystyle{\inf_{\|x\|=1}} \frac{1}{4S(\sqrt{h})}\big(\big\langle \big(A^*A-B^*B\big) x,x\big\rangle\big)^2 \end{equation*} for some $h>0$, where $\|\cdot\|,\,\,\,\omega(\cdot)$ and $S(\cdot)$denote the usual operator norm, numerical radius and the Specht'sratio, respectively. پرونده مقاله -
دسترسی آزاد مقاله
2 - Reverses of the first Hermite-Hadamard type inequality for the square operator modulus in Hilbert spaces
S. S. Dragomir‎Let $\left( H;\left\langle \cdot‎ ,‎\cdot \right\rangle \right)$ be a complex‎ ‎Hilbert space‎. ‎Denote by $\mathcal{B}\left( H\right)$ the Banach $C^{\ast }$-‎algebra of bounded linear operators on $H$‎. ‎For $A\in \mathcal{B}\l چکیده کامل‎Let $\left( H;\left\langle \cdot‎ ,‎\cdot \right\rangle \right)$ be a complex‎ ‎Hilbert space‎. ‎Denote by $\mathcal{B}\left( H\right)$ the Banach $C^{\ast }$-‎algebra of bounded linear operators on $H$‎. ‎For $A\in \mathcal{B}\left(‎H\right)$ we define the modulus of $A$ by $\left\vert A\right\vert‎ :‎=\left(‎A^{\ast }A\right) ^{1/2}$ and \ $\func{Re}A:=\frac{1}{2}\left( A^{\ast‎‎}+A\right)‎.‎$ In this paper we show among other that‎, ‎if $A,$ $B\in \mathcal{‎‎B}\left( H\right)$ with $0\leq m\leq \left\vert \left( 1-t\right)‎‎A+tB\right\vert ^{2}\leq M$ for all $t\in \left[ 0,1\right]‎,‎$ then \begin{align*}‎ ‎0& \leq \int_{0}^{1}f\left( \left\vert \left( 1-t\right) A+tB\right\vert‎‎^{2}\right) dt-f\left( \frac{\left\vert A\right\vert ^{2}+\func{Re}\left(‎‎B^{\ast }A\right)‎ +‎\left\vert B\right\vert ^{2}}{3}\right) \\‎ ‎& \leq 2\left[ \frac{f\left( m\right)‎ +‎f\left( M\right) }{2}-f\left( \frac{‎m+M}{2}\right) \right] 1_{H}‎ ‎\end{align*} ‎for operator convex functions $f:[0,\infty )\rightarrow \mathbb{R}$‎. ‎Applications for power and logarithmic functions are also provided‎. پرونده مقاله -
دسترسی آزاد مقاله
3 - A log-convex approach to Jensen-Mercer inequality
M. Davarpanah H. R. Moradi‎We obtain some new Jensen-Mercer type inequalities for log-convex functions‎. ‎Indeed‎, ‎we establish refinement and reverse for the Jensen-Mercer inequality for log-convex functions‎. ‎Several new Hermite-Hadamard and Fej\'er types of inequ چکیده کامل‎We obtain some new Jensen-Mercer type inequalities for log-convex functions‎. ‎Indeed‎, ‎we establish refinement and reverse for the Jensen-Mercer inequality for log-convex functions‎. ‎Several new Hermite-Hadamard and Fej\'er types of inequalities are also presented‎.‎ پرونده مقاله -
دسترسی آزاد مقاله
4 - (m1,m2)-Convexity and Some New Hermite-Hadamard Type Inequalities
Huriye KadakalIn this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean int چکیده کاملIn this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than with Hölder integral inequality and improwed power-mean inequality gives a better approach than with power-mean inequality. پرونده مقاله -
دسترسی آزاد مقاله
5 - On Hermite-Hadamard Type Inequalities for Co-ordinated Hyperbolic ρ-Convex Functions
Kubilay Özçelik Huseyin Budak S. Sever DragomirIn this study, we first introduce the co-ordinated hyperbolic ρ-convex functions. Then we establish some Hermite-Hadamard type inequalities for co-ordinated hyperbolic ρ-convex functions. The inequalities obtained in this study provide generalizations of some re چکیده کاملIn this study, we first introduce the co-ordinated hyperbolic ρ-convex functions. Then we establish some Hermite-Hadamard type inequalities for co-ordinated hyperbolic ρ-convex functions. The inequalities obtained in this study provide generalizations of some results given in earlier works. پرونده مقاله
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