OLYMPIC-REVENGE 2017 Problem 4

Let $f:\mathbb{R}_{+}^{*}$ $\rightarrow$ $\mathbb{R}_{+}^{*}$ such that $f'''(x)>0$ for all $x$ $\in$ $\mathbb{R}_{+}^{*}$ . Prove that: $f(a^{2}+b^{2}+c^{2})+2f(ab+bc+ac)$ $\geq$ $f(a^{2}+2bc)+f(b^{2}+2ca)+f(c^{2}+2ab)$ , for all $a,b,c$ $\in$ $\mathbb{R}_{+}^{*}$ .