Affiliations: Department of Mathematics, Ege University, İzmir, Turkey
Correspondence:
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Corresponding author. İbrahim Çanak, Department of Mathematics, Ege University, 35100 İzmir, Turkey. Tel.: +90 232 3115418; Fax: +90 232 3881036; E-mail: ibrahim.canak@ege.edu.tr.
Abstract: Let 0 ≠ p (x) be a nondecreasing real valued function on [0, ∞) such that p (0) =0 and
liminfx→∞p(λx)p(x)>1foreveryλ>1.
Given a fuzzy-number-valued continuous function f (x) on [0, ∞), we define
s(x):=∫0xf(t)dtandσ(x):=1p(x)∫0xs(t)dp(t),x>0.
It is known that the limit
limx→∞s(x)=μ
exists, then the limit
limx→∞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
limx→∞σ(x)=μ
follows from that of
limx→∞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.
Keywords: Fuzzy-number-valued functions, fuzzy Riemann-Stieltjes integral, Tauberian theorems, weighted mean method of integrals, slowly decreasing function
