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A note on “Some results on the IF-normed spaces”

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  • Saadati, Reza

Abstract

Recently, Lael and Nourouzi [Some results on the IF-normed spaces. Chaos, Solitons & Fractals 2006; doi:10.1016/j.chaos.2006.10.019] introduced and studied a new notation of IF-normed spaces by using the idea of intuitionistic fuzzy normed spaces due to Saadati and Park [On the intuitionistic fuzzy topological spaces. Chaos, Solitons & Fractals 2006;27:331–44], a special continuous t-norm i.e. min and a special continuous s-norm i.e. max. In this note, we consider the modified definition of IF-normed space i.e. LF-normed spaces and prove the open mapping and closed graph theorems for this space using arbitrary continuous t-norm.

Suggested Citation

  • Saadati, Reza, 2009. "A note on “Some results on the IF-normed spaces”," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 206-213.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:206-213
    DOI: 10.1016/j.chaos.2007.11.027
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    References listed on IDEAS

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    1. El Naschie, Mohamed Saladin, 2006. "The idealized quantum two-slit gedanken experiment revisited—Criticism and reinterpretation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 843-849.
    2. Saadati, Reza & Park, Jin Han, 2006. "On the intuitionistic fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 331-344.
    3. Gregori, V. & Romaguera, S. & Veeramani, P., 2006. "A note on intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 902-905.
    4. Saadati, Reza & Razani, Abdolrahman & Adibi, H., 2007. "A common fixed point theorem in L-fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 358-363.
    5. 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.
    6. El Naschie, M.S., 2006. "On two new fuzzy Kähler manifolds, Klein modular space and ’t Hooft holographic principles," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 876-881.
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    Cited by:

    1. 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.
    2. 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.

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