Iterative decodings used for turbo codes, concatenated codes and LDPC codes have been the main current of Coding Theory. Many researches have been done to improve the structure, algorithms and so on. But, the iterative process itself was not so much improved. On the other hand, in the field of nonlinear analysis, various iterative methods have been studied for nonlinear mappings. We consider the iterative decodings as nonlinear discrete dynamical systems in mathematics and apply iterative processes called Mann type iteration to the iterative decoding process. We will show, by using monotone operator theory, that the proposed method has more extensive stable domain than that of the conventional iterative process. Moreover, we will see the effect of proposed method in computer simulations.