Abstract
A fuzzy version of the Hahn-Banach theorem is proved based on the classical result. A comparison is also drawn with an earlier published result in this connection.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bachman, G., Narici, L.: Functional Analysis. Academic Press, New York (1966)
Dunford, N., Schwartz, J.T.: Linear Operators I. Wiley Interscience, Hoboken (1958)
Ghanim, M.H., Mashour, A.S.: Characterization of fuzzy topologies by s-neighbourhood systems. Fuzzy Sets and Systems 9, 211–213 (1983)
Katsaras, A.K., Liu, D.B.: Fuzzy Vector Spaces and Fuzzy Topological Vector Spaces. J. Math. Anal. Appl. 58, 135–146 (1977)
Katsaras, A.K.: Fuzzy Topological Vector Spaces I. Fuzzy Sets and Systems 6, 85–95 (1981)
Katsaras, A.K.: Fuzzy Topological Vector Spaces II. Fuzzy Sets and Systems 12, 143–154 (1984)
Kelley, J.L., Namioka, I.: Linear Topological Spaces. Van Nostrand, Princeton (1963)
Rhie, G.S., Hwang, I.A.: On the fuzzy Hahn-Banach Theorem - an analytic form. Fuzzy Sets and Systems 108, 117–121 (1999)
Taylor, A.E.: Introduction to Functional Analysis. Wiley, Hoboken (1958)
Warren, R.H.: Fuzzy topologies characterized by neighbourhood systems. Rocky Mountain Journal of Mathematics 9(4), 761–764 (1979)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Kotzé, W., Pinchuck, A. (2007). A Fuzzy Hahn-Banach Theorem. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_42
Download citation
DOI: https://doi.org/10.1007/978-3-540-72950-1_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72917-4
Online ISBN: 978-3-540-72950-1
eBook Packages: Computer ScienceComputer Science (R0)