A Tauberian theorem for the weighted mean method of improper integrals of fuzzy-number-valued functions

作者：Onder Zerrin; Canak Ibrahim^*

来源：Journal of Intelligent and Fuzzy Systems, 2017, 33(1): 293-303.

DOI：10.3233/JIFS-161596

• Fuzzy-number-valued functions
• fuzzy Riemann-Stieltjes integral
• Tauberian theorems
• weighted mean method of integrals
• slowly decreasing function

Let 0 not equal p(x) be a nondecreasing real valued function on [0,infinity) such that p(0) = 0 and
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Given a fuzzy-number-valued continuous function f (x) on [0,infinity), we define
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It is known that the limit lim(x ->infinity) s(x) = mu exists, then the limit lim(x ->infinity) sigma(x) = mu also exists. But the converse of this implication need not be satisfied in general.
In this paper, our goal is to find a condition under which the existence of lim(x ->infinity) sigma(x) = mu follows from that of lim(x ->infinity) s( x) = mu.
As special cases, we obtain some Tauberian conditions of slowly decreasing type and Landau type for the Cesaro summability method of improper integrals of fuzzy-number-valued functions.

• 出版日期2017