Improvement Sets and Convergence of Optimal Points

The aim of this paper is to give sufficient conditions for the existence of optimal points with respect to an improvement set, in the framework of Banach spaces and by using a recent definition of such sets, given by M.Chicco et al. and by C.Guti\ue9rrez et al. The study of an economic model is provided as example of application of our achievements. The lower and the upper convergence of optimal points of a convergent sequence of sets, in finite and infinite dimensional settings, are also considered, improving previous results. Finally, some sufficient conditions for the stability of optimal points are developed, discussing their importance via several examples