The proliferation of Quality of Service-aware applications in edge computing environments has created critical challenges in resource scheduling, particularly regarding energy optimization in resource-constrained infrastructures. As serverless computing paradigms extend to the edge, the integration of Dynamic Voltage and Frequency Scaling capabilities presents opportunities for significant energy savings while maintaining stringent performance requirements. However, existing resource scheduling approaches in serverless edge computing fail to exploit DVFS capabilities effectively, lacking unified frameworks that jointly optimize energy consumption and QoS compliance for deadline-sensitive applications. This thesis presents a novel resource scheduling framework for energy optimization of QoS-aware applications in DVFS-enabled serverless edge computing environments. The proposed approach develops a comprehensive system model encompassing a multi-tier architecture of IoT devices, edge nodes, fog nodes, and data center resources, where each computational tier features DVFS-enabled processors with discrete frequency levels. The resource scheduling problem is formulated as a Mixed Integer Linear Programming optimization that simultaneously addresses function placement and frequency selection decisions to minimize total system energy consumption while ensuring QoS requirements through deadline compliance. The solution employs a Deep Q-Network agent that learns optimal resource scheduling policies by incorporating DVFS decision-making into its action space and utilizing a multi-objective reward function that balances energy efficiency with QoS satisfaction. Comprehensive experimental evaluation using discrete-event simulation demonstrates that the proposed resource scheduling approach achieves substantial improvements across critical performance metrics. The DQN-based scheduler reduces energy consumption by up to approximately 33% compared to baseline algorithms. while maintaining superior QoS compliance through reduced deadline violations and improved response times. The integration of intelligent DVFS control with serverless function placement enables fine-grained energy optimization without compromising application performance requirements. These findings establish the effectiveness of deep reinforcement learning for resource scheduling in DVFS-enabled serverless edge environments, providing a practical framework for sustainable edge computing deployments that meet the demanding requirements of QoS-aware applications.