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On stability of a cubic functional equation in intuitionistic fuzzy normed spaces

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  • Mursaleen, M.
  • Mohiuddine, S.A.

Abstract

In this paper, we determine some stability results concerning the cubic functional equationf(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the cubic mappings and prove that the existence of a solution for any approximately cubic mapping implies the completeness of IFNS.

Suggested Citation

  • Mursaleen, M. & Mohiuddine, S.A., 2009. "On stability of a cubic functional equation in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2997-3005.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2997-3005
    DOI: 10.1016/j.chaos.2009.04.041
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    References listed on IDEAS

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    1. Saadati, Reza & Park, Jin Han, 2006. "On the intuitionistic fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 331-344.
    2. Mursaleen, M. & Mohiuddine, S.A., 2009. "Nonlinear operators between intuitionistic fuzzy normed spaces and Fréchet derivative," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1010-1015.
    3. El Naschie, M.S., 2009. "Arguments for the compactness and multiple connectivity of our cosmic spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2787-2789.
    4. Marek-Crnjac, L., 2009. "A short history of fractal-Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2697-2705.
    5. El Naschie, M.S., 2009. "On zero-dimensional points curvature in the dynamics of Cantorian-fractal spacetime setting and high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2725-2732.
    6. El Naschie, M.S., 2006. "Holographic dimensional reduction: Center manifold theorem and E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 816-822.
    7. Mursaleen, M. & Mohiuddine, S.A., 2009. "Statistical convergence of double sequences in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2414-2421.
    8. El Naschie, M.S., 2006. "Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1025-1033.
    9. Marek-Crnjac, L., 2009. "A Feynman path integral-like method for deriving the four dimensionality of spacetime from first principles," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2471-2473.
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    Cited by:

    1. Mohiuddine, S.A., 2009. "Stability of Jensen functional equation in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2989-2996.
    2. Abdulaziz M. Alanazi & G. Muhiuddin & K. Tamilvanan & Ebtehaj N. Alenze & Abdelhalim Ebaid & K. Loganathan, 2020. "Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods," Mathematics, MDPI, vol. 8(7), pages 1-14, June.

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