If $h_1$ and $h_2$ are admissible heuristic functions, prove that $h_3 = (c-1)\,h_1 + c\,h_2$, $0 < c < 1$, is also an admissible heuristic function.
The thing that I get stuck on, and maybe get a little tunnel-vision, is that $(c-1)$ is negative which prevents me from "building" the inequality starting from $h_1(n) \leq a(n)$, where $a(n)$ the actual cost to the end node. Any help with a mathematical explanation or using an example is greatly appreciated.
• It's a typo. It should have been $1-c$. People confirm it since the typo is in the source, but that doesn't mean it's not a typo. It's a classical example of the importance of having independent pieces of evidence. – Yuval Filmus Sep 6 '17 at 11:17