Hahn–Banach theorems in nonstandard normed interval spaces

The conventional Hahn–Banach extension theorem based on vector space has been widely used to obtain many important and interesting results in nonlinear analysis, vector optimization and mathematical economics. Although the interval space is not a real vector space, the Hahn–Banach extension theorems based on interval spaces and nonstandard normed interval spaces can still be derived in this paper, which also shows the possible applications by considering the interval-valued problems in nonlinear analysis, vector optimization and mathematical economics.