Hopf algebras arising from partial (co)actions

In this paper, extending the idea presented by M. Takeuchi in [13], we introduce the notion of partial matched pair $(H,L)$ involving the concepts of partial action and partial coaction between two Hopf algebras $H$ and $L$. Furthermore, we present necessary conditions for the corresponding bismash product $L\mathrm{\#}H$ to generate a new Hopf algebra and, as illustration, a family of examples is provided.