Existence and uniqueness of the solution of fuzzy-valued integral equations of mixed type (Q2805871)

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scientific article; zbMATH DE number 6580336
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Existence and uniqueness of the solution of fuzzy-valued integral equations of mixed type
scientific article; zbMATH DE number 6580336

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    13 May 2016
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    fuzzy-valued functions
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    fuzzy numbers
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    fuzzy Volterra integral equations
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    fuzzy Fredholm integral equations
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    existence
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    uniqueness
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    Existence and uniqueness of the solution of fuzzy-valued integral equations of mixed type (English)
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    Fuzzy Volterra integral equations were introduced by \textit{P. V. Subrahmanyam} and \textit{S. K. Sudarsanam} [Fuzzy Sets Syst. 81, No. 2, 237--240 (1996; Zbl 0884.45002)]. Their existence and uniqueness theorems are now generalized to the case of fuzzy Volterra-Fredholm integral equations (with double integrals).NEWLINENEWLINEReviewer's remark: 1. Theorem 3.2 contains a misprint (double meaning of \(n\)): a) \(n\) is the dimension of the space \(E^n\) of fuzzy numbers (from the beginning of the paper), b) \(n\) is a sufficiently large number. In Example 4.1 we get \(n=1\) in the case a) and \(n! > 12^n\) (e.g. \(n>33\)) in the case b). 2. A similar misprint is hidden in the proof of Theorem 3.1. 3. Both misprints are copied here from the generalized source paper [loc. cit.].
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