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In this article, we prove that the double inequality $$\alpha G(a,b)+(1-\alpha)C(a,b) 0$ with $a\neq b$ if and only if $\alpha\geq 5/9$ and $\beta\leq 1-1/[2\log(1+\sqrt{2})]=0.4327...$, where $G(a,b),C(a,b)$ and $M(a,b)$ are respectively the geometric, contra-harmonic and Neuman-S\'andor means of $a$ and $b$.

Optimal bounds for the Neuman-Sandor means in terms of geometric and contraharmonic means