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

Authors

  • 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.

DOI:

https://doi.org/10.17977/um067v6i32026p3

Keywords:

Fuzzy Banach Space, Solid Fuzzy Topology, Uniform Convergence, Fuzzy Norm, Fuzzy Integral Equation, Volterra Equation, Solidity, Fuzzy Functional Analysis

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.

References

Bag, T., & Samanta, S. K. (2003). Finite dimensional fuzzy normed linear spaces. The Journal of Fuzzy Mathematics, 11(3), 687–705.

Chang, C. L. (1968). Fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 24(1), 182–190.

Cheng, S. C., & Mordeson, J. N. (1994). Fuzzy linear operators and fuzzy normed linear spaces. Bulletin of the Calcutta Mathematical Society, 86(5), 429–436.

Das, N. R., & Das, P. (2018). Solid fuzzy topological spaces. Annals of Fuzzy Mathematics and Informatics, 15(2), 123–137.

Felbin, C. (1992). Finite dimensional fuzzy normed linear spaces. Fuzzy Sets and Systems, 48(2), 239–248.

Gregori, V., & Romaguera, S. (2004). Fuzzy metric spaces and fixed-point theorems. Fuzzy Sets and Systems, 144(3), 443–456.

Kaleva, O. (1987). Fuzzy differential equations. Fuzzy Sets and Systems, 24(3), 301–317.

Katsaras, A. K. (1984). Fuzzy topological vector spaces. Fuzzy Sets and Systems, 12(2), 143–154.

Kwon, Y. K. (2000). Fuzzy Volterra integral equations. Korean Journal of Computational & Applied Mathematics, 7(2), 421–428.

Nadaban, S. (2015). Fuzzy pseudo-normed spaces. International Journal of Computers Communications & Control, 10(6), 862–872.

Xiao, J. Z., & Zhu, X. H. (2005). Fuzzy normed spaces and its completion. Fuzzy Sets and Systems, 154(2), 275–283.

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.

Downloads

Published

31-03-2026

How to Cite

Rashid, M. A. ., & Mushatet, H. H. . (2026). Solid Structures in Fuzzy Banach Spaces: Topology of Uniform Convergence and Application to Fuzzy Integral Equations. Jurnal MIPA Dan Pembelajarannya, 6(3), 3. https://doi.org/10.17977/um067v6i32026p3

Issue

Vol. 6 No. 3 (2026): March

Section

Articles

License

Copyright (c) 2026 Murtadha Ali Rashid, Hasan H. Mushatet

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.