$m$-periodic Gorenstein objects

We present and study the concept of $m$-periodic Gorenstein objects relative to a pair $(\mathcal{A},\mathcal{B})$ of classes of objects in an abelian category, as a generalization of $m$-strongly Gorenstein projective modules over associative rings. We prove several properties in some cases where $(\mathcal{A},\mathcal{B})$ satisfies certain homological conditions, like for instance when $(\mathcal{A},\mathcal{B})$ is a GP-admissible pair. Connections to Gorenstein objects and Gorenstein homological dimensions relative to these pairs are also established.