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FUNDAMENTAL STABILITIES OF THE NONIC FUNCTIONAL EQUATION IN INTUITIONISTIC FUZZY NORMED SPACES

  • Bodaghi, Abasalt (Department of Mathematics Garmsar Branch Islamic Azad University) ;
  • Park, Choonkil (Research Institute for Natural Sciences Hanyang University) ;
  • Rassias, John Michael (Section of Mathematics and Informatics Pedagogical Department National and Capodistrian University of Athens)
  • Received : 2015.08.07
  • Published : 2016.10.31

Abstract

In the current work, the intuitionistic fuzzy version of Hyers-Ulam stability for a nonic functional equation by applying a fixed point method is investigated. This way shows that some fixed points of a suitable operator can be a nonic mapping.

Keywords

References

  1. T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems 151 (2005), no. 3, 513-547. https://doi.org/10.1016/j.fss.2004.05.004
  2. T. Bag and S. K. Samanta, Some fixed point theorems in fuzzy normed linear spaces, Inform. Sci. 177 (2007), no. 16, 3271-3289. https://doi.org/10.1016/j.ins.2007.01.027
  3. A. Bodaghi, Cubic derivations on Banach algebras, Acta Math. Vietnam. 38 (2013), no. 4, 517-528. https://doi.org/10.1007/s40306-013-0031-2
  4. A. Bodaghi, Stability of a quartic functional equation, The Scientific World J. 2014 (2014), Article ID 752146, 9 pages.
  5. A. Bodaghi, Intuitionistic fuzzy stability of the generalized forms of cubic and quartic functional equations, J. Intel. Fuzzy Syst. 30 (2016), 2309-2317. https://doi.org/10.3233/IFS-152001
  6. A. Bodaghi, I. A. Alias, and M. H. Ghahramani, Ulam stability of a quartic functional equation, Abstr. Appl. Anal. 2012 (2012), Article ID 232630, 9 pages.
  7. A. Bodaghi, S. M. Moosavi, and H. Rahimi, The generalized cubic functional equation and the stability of cubic Jordan *-derivations, Ann. Univ. Ferrara Sez. VII Sci. Mat. 59 (2013), no. 2, 235-250. https://doi.org/10.1007/s11565-013-0185-9
  8. A. Bodaghi and Gh. Zabandan, On the stability of quadratic (*-) derivations on (*-) Banach algebras, Thai J. Math. 12 (2014), no. 2, 343-356.
  9. L. Cadariu and V. Radu, Fixed points and the stability of quadratic functional equations, An. Univ. Timisoara, Ser. Mat.-Inform. 41 (2003), no. 1, 25-48.
  10. L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: A fixed point approach, Grazer Math. Ber. 346 (2004), 43-52.
  11. L. Cadariu and V. Radu, Fixed points and stability for functional equations in probabilistic metric and random normed spaces, Fixed Point Theory Appl. 2009 (2009), Article ID 589143, 18 pages.
  12. J. B. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305-309. https://doi.org/10.1090/S0002-9904-1968-11933-0
  13. J. X. Fang, On I-topology generated by fuzzy norm, Fuzzy Sets and Systems 157 (2006), no. 20, 2739-2750. https://doi.org/10.1016/j.fss.2006.03.024
  14. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  15. S. A. Mohiuddine and H. Sevli, Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space, J. Compu. Appl. Math. 235 (2011), 2137-214. https://doi.org/10.1016/j.cam.2010.10.010
  16. M. Mursaleen and Q. M. D. Lohani, Intuitionistic fuzzy 2-normed space and some related concepts, Chaos Solitons Fractals 42 (2009), no. 1, 224-234. https://doi.org/10.1016/j.chaos.2008.11.006
  17. J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals 22 (2004), no. 5, 1039-1046. https://doi.org/10.1016/j.chaos.2004.02.051
  18. J. M. Rassias and M. Eslamian, Fixed points and stability of nonic functional equation in quasi- ${\beta}$-normed spaces, Contemp. Anal. Appl. Math. 3 (2015), no. 2, 293-309.
  19. R. Saadati, A note on "Some results on the IF-normed spaces", Chaos Solitons Fractals 41 (2009), no. 1, 206-213. https://doi.org/10.1016/j.chaos.2007.11.027
  20. R. Saadati, Y. J. Cho, and J. Vahidi, The stability of the quartic functional equation in various spaces, Comput. Math. Appl. 60 (2010), no. 7, 1994-2002. https://doi.org/10.1016/j.camwa.2010.07.034
  21. R. Saadati and C. Park, Non-archimedean L-fuzzy normed spaces and stability of functional equations, Comput. Math. Appl. 60 (2010), no. 8, 2488-2496. https://doi.org/10.1016/j.camwa.2010.08.055
  22. R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals 27 (2006), no. 2, 331-344. https://doi.org/10.1016/j.chaos.2005.03.019
  23. R. Saadati, A. Razani, and H. Adibi, A common fixed point theorem in L-fuzzy metric spaces, Chaos Solitons Fractals 33 (2007), no. 2, 358-363. https://doi.org/10.1016/j.chaos.2006.01.023
  24. R. Saadati, S. Sedghi, and N. Shobe, Modified intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos Solitons Fractals 38 (2008), no. 1, 36-47. https://doi.org/10.1016/j.chaos.2006.11.008
  25. S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science Ed., Wiley, New York, 1940.
  26. T. Z. Xu, M. J. Rassias, and W. X. Xu, Stability of a general mixed additive-cubic functional equation in non-archimedean fuzzy normed spaces, J. Math. Phys. 51 (2010), no. 9, 093508, 19 pages.
  27. T. Z. Xu, M. J. Rassias, W. X. Xu, and J. M. Rassias, A fixed point approach to the intuitionistic fuzzy stability of quintic and sextic functional equations, Iran. J. Fuzzy Syst. 9 (2012), no. 5, 21-40.
  28. L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X

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