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February 25, 2026SHILAP Revista de lepidopterología0 citationsOpen Access

On Generalized Normed Spaces

NKNur Khusnussa'adah.S. SupamaAZAtok Zulijanto

Key Points

  • The aim is to introduce and define the concept of a G-normed space and explore its operators.
  • Defined the concept of G-normed spaces.
  • Introduced G-continuous and G-bounded linear operators.
  • Explored properties of these operators.
  • Proved a version of the Banach-Steinhaus Theorem for G-normed spaces.
  • Established the definitions and properties of G-continuous and G-bounded operators.
  • Formulated a new version of the Banach-Steinhaus Theorem for G-normed spaces.

Abstract

In this paper, we introduce a generalized normed space, which we refer to as a G-normed space. We define the concepts of a G-continuous and a G-bounded linear operator on this space and explore some related properties. Given the central role of the Banach-Steinhaus Theorem in the theory of normed spaces, particularly in the study of bounded linear operators, we conclude by formulating and proving a version of the Banach-Steinhaus Theorem for G-normed spaces.

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Cite This Study

Khusnussa'adah et al. (2026) studied this question.

synapsesocial.com/papers/699e912ef5123be5ed04e84dhttps://doi.org/10.22130/scma.2025.2056380.2113
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