A Tauberian theorem for the weighted mean method of improper integrals of fuzzy-number-valued functions
Makaleler > Tam Makale · 2017
Yazarlar: Zerrin ONDER, İbrahim ÇANAK
Journal of Intelligent & Fuzzy Systems, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Wos, 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.