Decomposition of $(\alpha -hg, \lambda)$ -continuity

In this new research paper we introduce and investigate the new kind of open sets $\alpha$ -Hg -open, $\sigma$-Hg -open, $\pi$ -Hg -open,$\beta$ -Hg - open and S - $\beta$ -Hg - open sets in hereditary generalized topological spaces. Moreover we introduce and study some new types of sets in HGT S. Also we obtained a decomposition of $( \alpha -Hg, \lambda) $-continuity and decompositions of $(g_μ, \lambda) $-continuity.