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

Shokoohi, Tahere; Modarres Mosadegh, Seyed Mohammad Sadegh; Karami, Azam

doi:10.22103/jmmr.2025.24728.1755

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

Document Type : Research Paper

Authors

Tahere Shokoohi

Seyed Mohammad Sadegh Modarres Mosadegh

Azam Karami

Department of Mathematics, Yazd University, Yazd, Iran

10.22103/jmmr.2025.24728.1755

Abstract

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.

Keywords

Interval analysis

Interval function

gH-diffrence

Intermediate value

time scales

Subjects

Analysis

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