In this article, we derive Chen’s inequalities involving ?-invariant ?M, Riemannian invariant ?(m1,?,mk), Ricci curvature, ?k(2?k?m), the scalar curvature and squared of mean for submanifolds generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application obtain inequality, first derived Chen inequality bi-slant submanifold Sasakian-space-forms.
