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Fréchet differentiation of nonlinear operators between fuzzy normed spaces

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  • Yilmaz, Yilmaz

Abstract

By the rapid advances in linear theory of fuzzy normed spaces and fuzzy bounded linear operators it is natural idea to set and improve its nonlinear peer. We aimed in this work to realize this idea by introducing fuzzy Fréchet derivative based on the fuzzy norm definition in Bag and Samanta [Bag T, Samanta SK. Finite dimensional fuzzy normed linear spaces. J Fuzzy Math 2003;11(3):687–705]. The definition is divided into two part as strong and weak fuzzy Fréchet derivative so that it is compatible with strong and weak fuzzy continuity of operators. Also we restate fuzzy compact operator definition of Lael and Nouroizi [Lael F, Nouroizi K. Fuzzy compact linear operators. Chaos, Solitons & Fractals 2007;34(5):1584–89] as strongly and weakly fuzzy compact by taking into account the compatibility. We prove also that weak Fréchet derivative of a nonlinear weakly fuzzy compact operator is also weakly fuzzy compact.

Suggested Citation

  • Yilmaz, Yilmaz, 2009. "Fréchet differentiation of nonlinear operators between fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 473-484.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:473-484
    DOI: 10.1016/j.chaos.2008.02.011
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    1. Lael, Fatemeh & Nourouzi, Kourosh, 2007. "Fuzzy compact linear operators," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1584-1589.
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    8. 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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