In this paper, we present the best possible parameters
$\alpha, \beta \in\mathbb{R}$
and
$\lambda, \mu\in(1/2, 1)$
such that the double inequalities
$\alpha N_{AQ}(a,b)+(1-\alpha)A(a,b)< T^{\ast}(a,b)0$
with
$a\neq b$
, where
$T^{\ast}(a,b)$
,
$A(a,b)$
,
$Q(a,b)$
and
$N_{QA}(a,b)$
are the Toader, arithmetic, quadratic, and Neuman means of a and b, respectively.
