Some fundamental theorems in the interval-valued functions and time scales

This research investigates the topological structure of the space of interval-valued functions equipped with an order relation defined by open balls. The aim is to establish analogues of fundamental theorems in calculus, including Bolzano’s theorem, the intermediate value theorem, and Rolle’s theorem, within this interval-valued function setting. Moreover, we introduce a novel extension of the Mean Value Theorem to the context of interval-valued functions on time scales. Our findings contribute to the development of interval analysis and its applications in various fields.

کلیدواژه ها:

Interval analysis ، Interval function ، gH-diffrence ، Intermediate value ، time scales