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Device-to-Device (D2D) communications emerged as a promising technology to improve the efficiency of 5G cellular networks. However, users should be encouraged to participate in content sharing and relaying, which are necessary for D2D communications. Thus, an incentive mechanism is essential to encourage the content owners and relay nodes to participate in D2D communications. In this study, a contract-based incentive mechanism is proposed for relaying D2D communications. In contrast to previous work, this mechanism simultaneously motivates both content owners and relays to participate in D2D communications. Furthermore, user mobility is considered in the proposed approach. Assuming that the devices in the network are mobile, mobility awareness can be effective in the performance of the proposed incentive mechanism since we need more appropriate contracts that are less likely to be violated …