We study monotonicity and continuity properties of the p-numerical radius \(\omega _p(T)\) and p-operator norm \(\Vert T\Vert _p\) of n-tuples \(T=(T_1,T_2,\ldots , T_n)\) of operators. It is shown that \(p\rightarrow n^{-1/p}\omega _p(T)\) and \(p\rightarrow n^{-1/p}\Vert T\Vert _p\) are increasing on \(p\in [1,\infty )\) , complementing the well known decreasing behavior of \(p\rightarrow w_p(T)\) and \(p\rightarrow \Vert T\Vert _p.\) We discuss uniform continuity of \( p\rightarrow \omega _{p}(T)\) . Convergence properties of the p-numerical radius and p-Crawford number of converging operator sequences are examined. The results obtained are supplemented by one application. In addition, we develop several inequalities for the p-numerical radius which extend and refine the existing classical numerical radius inequalities.
