Is $\sum_{i} \sum_{j} x_{ij} \log(\frac{a_{ij}}{\sum_{i}x_{ij}}+1) $ concave for $x_{ij} \in [0,1]$? I know that $\sum_{i} \sum_{j} x_{ij} \log(\frac{a_{ij}}{\sum_{i}x_{ij}})$ is concave for $x_{ij} \in [0,1]$ (It has been proven).
Any help is appreciated. Thanks.