Multimedia streaming has become integral to modern living, reshaping entertainment consumption, information access, and global engagement. The ascent of cloud computing, particularly serverless architectures, plays a pivotal role in this transformation, offering dynamic resource allocation, parallel execution, and automatic scaling-especially beneficial in HTTP Adaptive Streaming (HAS) applications. This study presents an event-driven serverless cloud edge platform with graphics processing units (GPUs), managed by Knative, tailored for video encoding. Two implementations of the High Efficiency Video Coding (HEVC) codec have been encapsulated in the functions: HEVC NVENC (Nvidia Encoder), that uses GPU acceleration, and x265 that only uses CPUs. Experiments focused on measuring the impact of replica requested resources on cold start, scalability and resource consumption with different allocated resources on slim and fat virtual machines (VMs). The best results are obtained when four slim replicas of the functions are deployed on a fat VM with a 8.4% reduction in encoding time for x265 and a 15.2% improvement for HEVC NVENC compared with other deployment scenarios. Comparatively, HEVC NVENC encoding is 8.3 times faster than x265. In multiresolution scenarios, GPU encoding drastically reduces segment encoding time by a factor of 12.4 between non-GPU and GPU-accelerated. These findings are important for live streaming applications where low latency is critical at all stages of the streaming process.