Open Access Research

Nonlinear -Fuzzy stability of cubic functional equations

Ravi P Agarwal1,2*, Yeol J Cho3, Reza Saadati4 and Shenghua Wang5

Author Affiliations

1 Department of Mathematics, Texas A&M University - Kingsville, Kingsville, TX 78363, USA

2 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

3 Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea

4 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, I.R. Iran

5 Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China

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Journal of Inequalities and Applications 2012, 2012:77 doi:10.1186/1029-242X-2012-77

Published: 2 April 2012

Abstract

We establish some stability results for the cubic functional equations

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and

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in the setting of various -fuzzy normed spaces that in turn generalize a Hyers-Ulam stability result in the framework of classical normed spaces. First, we shall prove the stability of cubic functional equations in the -fuzzy normed space under arbitrary t-norm which generalizes previous studies. Then, we prove the stability of cubic functional equations in the non-Archimedean -fuzzy normed space. We therefore provide a link among different disciplines: fuzzy set theory, lattice theory, non-Archimedean spaces, and mathematical analysis.

Mathematics Subject Classification (2000): Primary 54E40; Secondary 39B82, 46S50, 46S40.

Keywords:
stability; cubic functional equation; fuzzy normed space; -fuzzy set