The high mobility of unmanned aerial vehicles (UAVs) enables them to improve system throughput by establishing line-of-sight (LoS) links. Nevertheless, in urban environments, these LoS links can be disrupted by complex urban structures, leading to potential interference issues. Reconfigurable intelligent surfaces (RIS) provide an innovative approach to enhance communication performance by intelligently reflecting incident signals. Recent studies suggest that utilizing multi-antenna transmission can increase system efficiency, while single-antenna transmission may be more prone to interference. To address these challenges, this article introduces a RIS-assisted multiple-input single-output (MISO) UAV communication system. Our objective is to optimize the minimum user rate, thereby guaranteeing equitable communication for all users. Nevertheless, the non-convexity inherent in this optimization problem complicates the pursuit of a direct solution. Hence, we decompose the problem into four subproblems: user scheduling optimization, RIS phase-shift optimization, UAV trajectory optimization, and UAV transmit beamforming optimization. To obtain suboptimal solutions, we have developed an alternating iterative optimization algorithm for addressing the four subproblems. Numerical results demonstrate that our algorithm effectively boosts the minimum user rate of the entire system.