Renyi mutual information is an important information quantity in study of error exponent of noisy channel coding. In quantum information theory, this quantity has multiple noncommutative generalizations which found useful in different setting. In this talk, I will present an application of noncommutative $L_p$ space to prove the certain convexity of quantum Renyi type mutual information. This is a joint work with Hao-Chung Cheng and Min-Hsiu Hsieh.