Brouwer’s Fixed Point Theorem and Open Mapping Theorem in Hemi-Normed Spaces

Liaqat Ali, Muhammad Aslam, Ghulam Farid and Hala H. Taha

Journal of Mathematics, 2026, vol. 2026, 1-7

Abstract: This paper aims for the further development of hemi-normed spaces, which is a proper extension of normed spaces. In this regard, we establish some fundamental results of functional analysis, including Brouwer’s theorem and Schauder’s fixed point theorem for hemi-normed spaces. We also prove that every surjective continuous linear operator from a hemi-normed space onto a hemi-Banach space is open, leading to generalized forms of the Open Mapping, Bounded Inverse, and Closed Graph theorems.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7711006

DOI: 10.1155/jom/7711006

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