Abstract and Applied Analysis

The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited

Carmen Alegre and Salvador Romaguera

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Abstract

This paper deals with fuzzy normed spaces in the sense of Cheng and Mordeson. We characterize fuzzy norms in terms of ascending and separating families of seminorms and prove an extension theorem for continuous linear functionals on a fuzzy normed space. Our result generalizes the classical Hahn-Banach extension theorem for normed spaces.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 151472, 7 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277019

Digital Object Identifier
doi:10.1155/2014/151472

Mathematical Reviews number (MathSciNet)
MR3216032

Zentralblatt MATH identifier
07021816

Citation

Alegre, Carmen; Romaguera, Salvador. The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited. Abstr. Appl. Anal. 2014 (2014), Article ID 151472, 7 pages. doi:10.1155/2014/151472. https://projecteuclid.org/euclid.aaa/1412277019


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