Tauberian Theorems for the Product of Borel and Hölder Summability Methods
نویسنده
چکیده
In this paper we prove some Tauberian theorems for the product of Borel and Hölder summability methods which improve the classical Tauberian theorems for the Borel summability method. Mathematics Subject Classification 2010: 40E05, 40G05, 40G10.
منابع مشابه
H"{o}lder summability method of fuzzy numbers and a Tauberian theorem
In this paper we establish a Tauberian condition under which convergence follows from H"{o}lder summability of sequences of fuzzy numbers.
متن کاملSome conditions under which slow oscillation of a sequence of fuzzy numbers follows from Ces`{a}ro summability of its generator sequence
Let $(u_n)$ be a sequence of fuzzy numbers. We recover the slow oscillation of $(u_n)$ of fuzzy numbers from the Ces`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. Further, fuzzy analogues of some well known classical Tauberian theorems for Ces`{a}ro summability method are established as particular cases.
متن کاملOne-sided Tauberian Theorems for Dirichlet Series Methods of Summability
We extend recently established two-sided or O-Tauberian results concerning the summability method Dλ,a based on the Dirichlet series ∑ ane−λnx to one-sided Tauberian results. More precisely, we formulate one-sided Tauberian conditions, under which Dλ,a-summability implies convergence. Our theorems contain various known results on power series methods of summability and, in the so-called high in...
متن کاملA One-sided Theorem for the Product of Abel and Cesàro Summability Methods
In this paper, a one-sided condition is given to recover .C; ̨/ summability of a sequence from its .A/.C; ̨C 1/ summability. Our result extends and generalizes the well known classical Tauberian theorems given for Abel and Cesàro summability methods. 2010 Mathematics Subject Classification: 40E05; 40G05; 40G10
متن کاملA Tauberian theorem for $(C,1,1)$ summable double sequences of fuzzy numbers
In this paper, we determine necessary and sufficient Tauberian conditions under which convergence in Pringsheim's sense of a double sequence of fuzzy numbers follows from its $(C,1,1)$ summability. These conditions are satisfied if the double sequence of fuzzy numbers is slowly oscillating in different senses. We also construct some interesting double sequences of fuzzy numbers.
متن کامل