Inverse cosine convex functions: Algebraic, geometric, and analytic perspectives

In this article, we investigate a new class of convexity named inverse cosine convex functions (ICCF). We explore and examine some algebraic and geometric features by presenting the graphs of several significant ICCF functions for visual demonstration. By using this proposed class of functions, we derive the Hermite–Hadamard (HH) inequality and certain refinements applicable to functions whose first derivative in absolute value is an ICCF. To derive the main consequences, we mainly use Hölder's, Hölder–İşcan, and power‐mean integral inequalities. Furthermore, it is proved that the results obtained using Hölder–İşcan and improved power‐mean integral inequalities have better approximations compared to other techniques. This novel idea of inverse cosine convexity allows us to explore new horizons of research and may motivate researchers to investigate such classes of convexity.