In this article, we present some new inequalities for numerical radius of Hilbert space operators via convex functions. Our results generalize and improve earlier results by El-Haddad and Kittaneh. Among several results, we show that if $A\in \mathbb{ B}\left( \mathcal{ H} \right)$ and $r\ge 2$, then \[{ { w}^{ r}}\left( A \right)\le { { \left\| A \right\|}^{ r}}-\underset{ \left\| x \right\|=1}{ \mathop{ \inf }}\,{ { \left\| { { \left| \left| A \right|-w\left( A \right) \right|}^{ \frac{ r}{ 2}}}x \right\|}^{ 2}}\] where $w\left( \cdot \right)$ and $\left\| \cdot \right\|$ denote the numerical radius and usual operator norm, respectively.
Categories: math.FA