Fréchet differentiation of nonlinear operators between fuzzy normed spaces

Yilmaz Yilmaz

Chaos, Solitons & Fractals, 2009, vol. 41, issue 1, 473-484

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.

Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077908000684
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:41:y:2009:i:1:p:473-484

DOI: 10.1016/j.chaos.2008.02.011

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().