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, 2026)
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.