## Abstract and Applied Analysis

### On the Intuitionistic Fuzzy Stability of Ring Homomorphism and Ring Derivation

#### Abstract

We take into account the stability of ring homomorphism and ring derivation in intuitionistic fuzzy Banach algebra associated with the Jensen functional equation. In addition, we deal with the superstability of functional equation $f(xy)=xf(y)+f(x)y$ in an intuitionistic fuzzy normed algebra with unit.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 192845, 8 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393448677

Digital Object Identifier
doi:10.1155/2013/192845

Mathematical Reviews number (MathSciNet)
MR3096811

Zentralblatt MATH identifier
1297.39037

#### Citation

Roh, Jaiok; Chang, Ick-Soon. On the Intuitionistic Fuzzy Stability of Ring Homomorphism and Ring Derivation. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 192845, 8 pages. doi:10.1155/2013/192845. https://projecteuclid.org/euclid.aaa/1393448677

#### References

• S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, NY, USA, 1960.
• D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 27, pp. 222–224, 1941.
• T. Aoki, “On the stability of the linear transformation in Banach spaces,” Journal of the Mathematical Society of Japan, vol. 2, pp. 64–66, 1950.
• T. M. Rassias, “On the stability of the linear mapping in Banach spaces,” Proceedings of the American Mathematical Society, vol. 72, no. 2, pp. 297–300, 1978.
• R. Badora, “On approximate ring homomorphisms,” Journal of Mathematical Analysis and Applications, vol. 276, no. 2, pp. 589–597, 2002.
• D. G. Bourgin, “Approximately isometric and multiplicative transformations on continuous function rings,” Duke Mathematical Journal, vol. 16, pp. 385–397, 1949.
• R. Badora, “On approximate derivations,” Mathematical Inequalities & Applications, vol. 9, no. 1, pp. 167–173, 2006.
• A. K. Mirmostafaee and M. S. Moslehian, “Fuzzy almost quadratic functions,” Results in Mathematics, vol. 52, no. 1-2, pp. 161–177, 2008.
• A. K. Mirmostafaee and M. S. Moslehian, “Fuzzy versions of Hyers-Ulam-Rassias theorem,” Fuzzy Sets and Systems, vol. 159, no. 6, pp. 720–729, 2008.
• S. A. Mohiuddine, “Stability of Jensen functional equation in intuitionistic fuzzy normed space,” Chaos, Solitons & Fractals, vol. 42, no. 5, pp. 2989–2996, 2009.
• S. A. Mohiuddine, M. Cancan, and H. Şevli, “Intuitionistic fuzzy stability of a Jensen functional equation via fixed point technique,” Mathematical and Computer Modelling, vol. 54, no. 9-10, pp. 2403–2409, 2011.
• S. A. Mohiuddine and H. Ševli, “Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2137–2146, 2011.
• M. Mursaleen and S. A. Mohiuddine, “On stability of a cubic functional equation in intuitionistic fuzzy normed spaces,” Chaos, Solitons & Fractals, vol. 42, no. 5, pp. 2997–3005, 2009.
• R. Saadati and J. H. Park, “On the intuitionistic fuzzy topological spaces,” Chaos, Solitons & Fractals, vol. 27, no. 2, pp. 331–344, 2006.
• B. Dinda, T. K. Samanta, and U. K. Bera, “Intuitionistic fuzzy Banach algebra,” Bulletin of Mathematical Analysis and Applications, vol. 3, no. 3, pp. 273–281, 2011.