Abstract In this paper we study the behavior of holomorphic mappings on A -compact sets. Motivated by the recent work of Aron, Caliskan, Garcia and Maestre (2016), we give several conditions (on the holomorphic mappings and on the λ-Banach operator ideal A ) under which A -compact sets are preserved. Appealing to the notion of tensor stability for operator ideals, we first address the question in the polynomial setting. Then, we define a radius of ( A ; B ) -compactification that permits us to tackle the analytic case. Our approach, for instance, allows us to show that the image of any ( p , r ) -compact set under any holomorphic function (defined on any open set of a Banach space) is again ( p , r ) -compact.