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Hasan H. Mushatet
General Directorate of Education in Karbala, Ministry of Education, Karbala, Iraq.
Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Education Energy Immunology & microbiology Materials Science & Nanotechnology Mathematics

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Solid Structures in Fuzzy Banach Spaces: Topology of Uniform Convergence and Application to Fuzzy Integral Equations Murtadha Ali Rashid; Hasan H. Mushatet; Murtadha Ali Rashid; Hasan H. Mushatet
Jurnal MIPA dan Pembelajarannya Vol. 6 No. 3 (2026): March
Publisher : Universitas Negeri Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17977/um067v6i32026p3

Abstract

This paper introduces and studies the notion of solidity in fuzzy Banach spaces. A fuzzy Banach space is called solid if the fuzzy topology is compatible with the vector structure in a uniformly bounded manner: multiplication by null sequence uniformly. We construct a natural matric that induces the fuzzy topology, prove completeness and relative compactness theorems, and provide original examples including spaces of fuzzy-valued functions and sequence spaces. An application to fuzzy Volterra integral equations is given using the Banach fixed point theorem. . The results extend classical Banach space theory to the fuzzy setting while preserving key properties such as metrizability, the Hahn-Banach extension (under solidity), and the Arzela-Ascoli characterization.
Co-Authors Hasan H. Mushatet Murtadha Ali Rashid Murtadha Ali Rashid