Standard Power Function, Absolute-Value Power Function, and Zhang Power Function

Power functions play a fundamental role in mathematical analysis and applied sciences. Among them, the standard power function (SPF), and the absolute-value power function (AVPF), exhibit distinct mathematical properties and applications. Additionally, to handle time-varying inequality-constrained optimization problems, we propose the concept of Zhang power function (ZPF), and investigate its specific forms as well as graphs. This paper thus explores their (i.e., SPF, AVPF, and ZPF's) definitions, expressions, differentiability, derivatives, symmetry, and their relationships. The research findings provide valuable information for the proposal and future applications of the Zhang power function.