@article{article_602415, title={Some generalized numerical radius inequalities involving Kwong functions}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={48}, pages={951–958}, year={2019}, author={Bakherad, Mojtaba}, keywords={numerical radius,Hadamard product,operator monotone,Kwong function}, abstract={We prove several numerical radius inequalities involving positive semidefinite matrices via the Hadamard product and Kwong functions. Among other inequalities, it is shown that if   $X$ is an arbitrary $n\times n$ matrix and $A,B$ are positive semidefinite, then <br />\[ \omega(H_{f,g}(A))\leq k\, \omega(AX+XA), \] <br /> which is equivalent to <br />\[\omega\big(H_{f,g}(A,B)\pm H_{f,g}(B,A)\big)\leq k’\,\left\{\omega((A+B)X+X(A+B))+\omega((A-B)X-X(A-B))\right\},\] <br /> where  $f$ and $g$ are two continuous functions on $(0,\infty)$ such that $h(t)={f(t)\over g(t)}$ is Kwong, $k=\max\left\{f(\lambda)g(\lambda)\over \lambda}: {\lambda\in\sigma(A)}\right\}$ and $k’=\max\left\{f(\lambda)g(\lambda)\over \lambda}: {\lambda\in\sigma(A)\cup\sigma(B)}\right\}$. <br />}, number={4}, publisher={Hacettepe University}