Tietjens' Inequality

Tietjens' Inequality provides a bound in the context of complex analysis, specifically relating to the behavior of holomorphic (complex differentiable) functions within a disk. It states that for any such function that maps the unit disk into itself, the difference in the function's values at two points inside the disk is limited by a factor depending on the points' positions. Essentially, it offers a precise way to measure how much the function can "stretch" or "distort" distances within the disk, ensuring the function remains controlled and well-behaved throughout its domain.