Recommender systems suggest the users with the most appropriate and accurate recommendations by reviewing and exploring user-related information (user's preferences and interests) from the user's previous experiences. Although recommender systems have been studied by many researchers in recent years, a few of them have considered the problem of balancing fairness and accuracy in dynamic recommender systems, where the interests of users change, and new items are added over time to the list of existing items. To resolve this problem, we propose a multi-objective deep reinforcement learning framework based on the actor-critic method, called \textit{FairAC}, which considers fairness in recommender systems in a dynamic environment. We conducted extensive experiments on real-world datasets. The results show that the proposed approach provides accurate and fair recommendations and surpassing the performance of prior studies by approximately 10\% in terms of both accuracy and fairness.