A Tauberian theorem for the weighted mean method of improper integrals of fuzzy-number-valued functions
Makaleler > Tam Makale · 2017
Yazarlar: Zerrin Önder, İbrahim ÇANAK
Journal of Intelligent and Fuzzy Systems, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Scopus, 2017, cilt 33, ss 293-303
DOI: 10.3233/JIFS-161596
Özet
Let 0 ≠ p (x) be a nondecreasing real valued function on [0, ∞) such that p (0) =0 and lim inf x → ∞ p (λ x) p (x) > 1 for every λ > 1. Given a fuzzy-number-valued continuous function f (x) on [0, ∞), we define s (x): = ∫ 0 x f (t) dt and σ (x): = 1 p (x) ∫ 0 x s (t) dp (t), x > 0. It is known that the limit lim x → ∞ s (x) = μ exists, then the limit lim x → ∞ σ (x) = μ 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 → ∞ σ (x) = μ follows from that of lim x → ∞ s (x) = μ. As special cases, we obtain some Tauberian conditions of slowly decreasing type and Landau type for the Cesàro summability method of improper integrals of fuzzy-number-valued functions.