Given an open subset U of a complex Banach space E, a weight v on U, and a complex Banach space F, let \(\mathcal {H}^\infty _v(U,F)\) denote the Banach space of all weighted holomorphic mappings \(f:U\rightarrow F\) , under the weighted supremum norm \(\left\| f\right\| _v:=\sup \left\{ v(x)\left\| f(x)\right\| :x\in U\right\} \) . In this paper, we introduce and study the classes of weighted holomorphic mappings \(\mathcal {H}^\infty _{v\mathcal {K}_{p}}(U,F)\) (resp., \(\mathcal {H}^\infty _{v\mathcal {K}_{wp}}(U,F)\) and \(\mathcal {H}^\infty _{v\mathcal {K}_{up}}(U,F)\) ) for which the set (vf)(U) is relatively p-compact (resp., relatively weakly p-compact and relatively unconditionally p-compact). We prove that these mapping classes are characterized by p-compact (resp., weakly p-compact and unconditionally p-compact) linear operators defined on a Banach predual space of \(\mathcal {H}^\infty _v(U)\) by linearization. We show that \(\mathcal {H}^\infty _{v\mathcal {K}_{p}}\) (resp., \(\mathcal {H}^\infty _{v\mathcal {K}_{wp}}\) and \(\mathcal {H}^\infty _{v\mathcal {K}_{up}}\) ) is a Banach ideal of weighted holomorphic mappings which is generated by composition with the ideal of p-compact (resp., weakly p-compact and unconditionally p-compact) linear operators and contains the Banach ideal of all right p-nuclear weighted holomorphic mappings. We also prove that these weighted holomorphic mappings can be factorized through a quotient space of \(l_{p^*}\) , and \(f\in \mathcal {H}^\infty _{v\mathcal {K}_{p}}(U,F)\) (resp., \(f\in \mathcal {H}^\infty _{v\mathcal {K}_{up}}(U,F))\) if and only if its transposition \(f^t\) is quasi p-nuclear (resp., quasi unconditionally p-nuclear).
