Low-dose x-ray computed tomography (LDCT) is desirable for reduced patient dose. This work develops new image reconstruction methods with deep learning (DL) regularization for LDCT. Our methods are based on the unrolling of a proximal forward-backward splitting (PFBS) framework with data-driven image regularization via deep neural networks. In contrast to PFBS-IR, which utilizes standard data fidelity updates via an iterative reconstruction (IR) method, PFBS-AIR involves preconditioned data fidelity updates that fuse the analytical reconstruction (AR) and IR methods in a synergistic way, i.e. fused analytical and iterative reconstruction (AIR). The results suggest that the DL-regularized methods (PFBS-IR and PFBS-AIR) provide better reconstruction quality compared to conventional methods (AR or IR). In addition, owing to the AIR, PFBS-AIR noticeably outperformed PFBS-IR and another DL-based postprocessing method, FBPConvNet.