The class of strongly quasiconvex functions was introduced in the famous paper of B.T. Polyak in 1966. It is the natural extension of the class of strongly convex functions, its applications emcompasses different problems from mathematical sciences, economics and engineering among others and, furthermore, they are especially useful for algorithms purposes. In this talk, we present an overview on strongly quasiconvex functions from the open question regarding the existence of solutions for the minimization problem until recent improvements. As a consequence, we study properties for the proximity operator and its applications in proximal point algorithms. Finally, we present new characterizations for differentiable strongly quasiconvex functions and a new class of functions which are strongly quasiconvex.
