Abstract
In the present note, we study epsilon-LP-Sasakian 3-manifolds M-3(epsilon) whose metrics are conformal eta-Ricci-Yamabe solitons (in short, CERYS), and it is proven that if an M-3(epsilon) with a constant scalar curvature admits a CERYS, then epsilon(U)zeta is orthogonal to zeta if and only if lambda-epsilon sigma=-2 epsilon l+mr/2+1/2p+2/3. Further, we study gradient CERYS in M-3(epsilon) and proved that an M-3(epsilon) admitting gradient CERYS is a generalized conformal eta-Einstein manifold; moreover, the gradient of the potential function is pointwise collinear with the Reeb vector field zeta. Finally, the existence of CERYS in an M-3(epsilon) has been drawn by a concrete example.