On nonlinear equations for fuzzy mappings in probabilistic normed spaces (Q1867645)
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scientific article; zbMATH DE number 1891654
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On nonlinear equations for fuzzy mappings in probabilistic normed spaces |
scientific article; zbMATH DE number 1891654 |
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On nonlinear equations for fuzzy mappings in probabilistic normed spaces (English)
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2 April 2003
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The author extends the results of \textit{Y. J. Cho}, \textit{H. J. Huang} and \textit{S. M. Kang} [ibid. 110, 115-122 (2000; Zbl 0949.47059)] showing that their concept of a probabilistic \(\psi\)-\(g\)-contractor couple is a particular case of the concept of a probabilistic \(\psi\)-contractor couple given in this paper. Then results of existence of solutions and convergence theorems of solutions of nonlinear equations for fuzzy mappings in Menger PN-spaces are obtained from analogous results for (non-fuzzy) set-valued nonlinear operators in the same spaces using this new concept.
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Menger PN-space
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probabilistic \(\Psi\)-contractor couple
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fuzzy mapping
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nonlinear equations
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