  In this paper, we achieve new and improved numerical radius inequalities of
operators defined on a Hilbert space by using Orlicz function and
Hermite-Hadamard inequality. The upper bounds of various inequalities involving
numerical radii have been obtained. Finally, we compute an upper bound of the
numerical radius for block matrices of the form $\begin{bmatrix}O & P\\Q & O
\end{bmatrix}$, where $P, Q$ are any bounded linear operators on a Hilbert
space.
