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

Author

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  • Liaqat Ali
  • Muhammad Aslam
  • Ghulam Farid
  • Hala H. Taha

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.

Suggested Citation

  • Liaqat Ali & Muhammad Aslam & Ghulam Farid & Hala H. Taha, 2026. "Brouwer’s Fixed Point Theorem and Open Mapping Theorem in Hemi-Normed Spaces," Journal of Mathematics, Hindawi, vol. 2026, pages 1-7, August.
    • Handle: RePEc:hin:jjmath:7711006
    DOI: 10.1155/jom/7711006
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