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

Document Type : Research Paper

Authors

Department of Mathematics, Yazd University, Yazd, Iran

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.

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References

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Journal of Mahani Mathematical Research
Volume 15, Issue 1 - Serial Number 33
January 2026
Pages 281-302

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History

  • Receive Date: 24 January 2025
  • Revise Date: 19 June 2025
  • Accept Date: 18 August 2025

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