1. Project Management Institute. (2013). A Guide to the Project Management Body of Knowledge (PMBOK® Guide) (5th ed.). Project Management Institute.
Section 8.2
Page 242: "Perform Quality Assurance is the process of auditing the quality requirements and the results from quality control measurements to ensure that appropriate quality standards and operational definitions are used." This definition directly matches the question's wording.
2. Project Management Institute. (2017). A Guide to the Project Management Body of Knowledge (PMBOK® Guide) (6th ed.). Project Management Institute.
Section 8.2
Page 288: The process was renamed to "Manage Quality." Its purpose is described as translating the quality management plan into executable quality activities.
Section 8.2.2.3
Page 294: Under Tools and Techniques
"Audits" are defined as a "structured
independent process used to determine if project activities comply with organizational and project policies
processes
and procedures." This confirms the auditing function is central to this process.