Convexity, Markov Operators, Approximation, and Related Optimization

The present review paper provides recent results on convexity and its applications to the constrained extension of linear operators, motivated by existence subgradients continuous convex Markov moment problem related approximation using Krein–Milman theorem, optimization, polynomial unbounded subsets. In many cases, Mazur–Orlicz theorem also leads operators as solutions. common point all these is Hahn–Banach consequences, supplied specific in approximation. All theorems or their proofs essentially involve notion convexity.