Solid Structures in Fuzzy Banach Spaces: Topology of Uniform Convergence and Application to Fuzzy Integral Equations

Murtadha Ali Rashid (General Directorate of Education in Karbala, Ministry of Education, Karbala, Iraq.)
Hasan H. Mushatet (General Directorate of Education in Thi-Qar, Ministry of Education, Thi-Qar, Iraq.)
Murtadha Ali Rashid
Hasan H. Mushatet (General Directorate of Education in Karbala, Ministry of Education, Karbala, Iraq.)

Jurnal MIPA dan Pembelajarannya
Vol. 6 No. 3 (2026): March

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.