The barriers to improving computers’ performance have led to the emergence of new computing paradigms and technologies. Among these, the memristors are of great concern. In addition to storing data, memristors can perform logical operations and are proper for In-Memory Computation (IMC). Furthermore, approximate computing is an emerging paradigm introduced to improve performance by reducing the accuracy of calculations in error-resistant applications. These two concepts are combined and presented in four serial Material Implication (IMPLY)-based approximate full adders. In addition, to the positive features of the serial method, the proposed circuits reduce the number of calculation steps by 7%-43%, and the energy consumption improves by 56%-68% compared to the existing exact full adders. The accuracy loss of proposed circuits in different simulated scenarios combining exact and approximate adders are analyzed. Four different image processing applications are applied to ensure the proper functionality of the proposed circuits. The results indicate that in most scenarios, the quality of the images is acceptable, and the Peak Signal-to-Noise Ratio (PSNR) criterion is more than 30 dB.