Sharp bounds for Toader mean in terms of arithmetic, quadratic, and Neuman means.

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 $\alpha N_{AQ}(a,b)+(1-\alpha)A(a,b)< T^{\ast}(a,b)<\beta N_{AQ}(a,b)+(1-\beta)A(a,b)$, $Q[\lambda a+(1-\lambda)b, \lambda b+(1-\lambda)a]< T^{\ast}(a,b)< Q[\mu a+(1-\mu)b, \mu b+(1-\mu)a] $ hold for all $a, b>0$ 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. [ABSTRACT FROM AUTHOR]