Jensenaffine

Jensenaffine is a term used in mathematical literature to describe a concept that couples affine transformations with ideas from Jensen's inequality in convex analysis. The term is not standardized across sources and may be used in slightly different ways.

Generally, a Jensenaffine map refers to an affine operator that is employed to study Jensen-type bounds or to construct affine estimators for convex functions. In practice, such maps are used to obtain affine minorants or majorants of a convex function, in a way that aligns with the linear structure of the problem. This perspective highlights how affine geometry interacts with Jensen's inequality when forming expected-value bounds.

Applications of the concept appear in optimization, economic theory, and risk assessment, where affine envelopment and convexity play a central role. Because the phrase is informal in many texts, exact definitions can vary; readers are advised to consult the specific source for the intended meaning in that context.

See also: Jensen's inequality, affine transformation, convex analysis, supporting hyperplane. The term is sometimes encountered in lecture notes, survey articles, and research papers exploring the interface of convexity and affine mappings.