Asymptotic analysis and the Weierstrass theorem in dual spaces

Abstract

In this paper, we introduce a new concept of asymptotic function to derive the Weierstrass theorem for transfer weakly lower continuous functions without coercivity condition in dual spaces that are endowed with the weak⁎ topology. Moreover, by this asymptotic function we establish a necessary and sufficient condition for a minimization problem within the framework of transfer weakly lower continuous and quasiconvex functions in dual spaces. © 2025 Elsevier Inc.