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In this paper, we study the concept of soft sets which is introduced by Molodtsov $[5]$ and the notion of soft continuity is introduced by Zorlutuna et al. $[8]$. We give the definition of $(\tau_{1},\tau_{2})$ - semi open soft ( resp. $(\tau_{1},\tau_{2})$ - pre open soft, $(\tau_{1},\tau_{2})$ - $\alpha$ - open soft, $(\tau_{1},\tau_{2})$ - $\beta$ - open soft ) set via two soft topologies. The aim of this paper is to introduce mixed semi - soft ( resp. mixed pre - soft, mixed $\alpha$ - soft, mixed $\beta$ - soft ) continuity between two soft topological spaces $(X,\tau_{1},A), (X,\tau_{2},A)$ and a soft topological space $(Y,\tau,B)$. Also we prove that a function is mixed $\alpha$ - soft continuous if and only if it is both mixed pre - soft continuous and mixed semi - soft continuous.

A decomposition of some types of mixed soft continuity in soft topological spaces