  Let $\Lambda(1,n)$ be the $(1,n)$-th Fourier coefficients of
$SL(3,\mathbb{Z})$ Hecke-Maass cusp form and $d_3(n)$ denotes the triple
divisor function. This paper establishes non-trivial bounds for the averages of
these arithmetic functions over polynomials in three variables having mixed
powers and over quadratic forms.
