The concepts of weighted numerical radius has been defined in recent times. In this article, we obtain several upper bound for weighted numerical radius of operators and $2 \times 2$ operator matrices which generalize and improves some well known famous inequality for classical numerical radius. We also obtain an upper bound for the weighted numerical radius of the Aluthge transformation, $\tilde{ T}$ of an operator $T \in \mathcal{ B}(\mathcal{ H}),$ where $\tilde{ T} = |T|^{ 1/2} U |T|^{ 1/2}$ and $T = U |T|$ be the canonical polar decomposition of $T.$
Categories: math.FA