Ümit Totur

A Tauberian theorem with a generalized one-sided condition.

We prove a Tauberian theorem to recover moderate oscillation of a real sequence u=(un) out of Abel limitability of the sequence (Vn(1)(Δu)) and some additional condition on the general control modulo of oscillatory behavior of integer order of u=(un).

Tauberian theorems for Abel limitability method

This paper addresses conditions for the Abel method of limitability to imply convergence and subsequential convergence.

Tauberian conditions for Cesaro summability of integrals

In this paper we generalize some classical type Tauberian theorems given for Cesaro summability of integrals.

A Tauberian theorem for Cesàro summability of integrals

Abstract In this paper we give a proof of the generalized Littlewood Tauberian theorem for Cesaro summability of improper integrals.

Alternative proofs of some classical type Tauberian theorems for the Cesàro summability of integrals

Abstract In this paper, we give alternative proofs of some classical type Tauberian theorems for the Cesaro summability of improper integrals.

One-sided Tauberian conditions for (C,1) summability method of integrals

Abstract Let f be a real valued function which is continuous on [ 0 , ∞ ) . In this paper we prove a Tauberian-like theorem to retrieve slow oscillation of s ( x ) = ∫ 0 x f ( t ) d t out of its ( C , 1 ) summability of the generator function v 1 ( x ) and some additional conditions. As a corollary we recover convergence of s ( x ) .

Subsequential Convergence Conditions

Let be a sequence of real numbers and let be any regular limitable method. We prove that, under some assumptions, if a sequence or its generator sequence generated regularly by a sequence in a class of sequences is a subsequential convergence condition for, then for any integer, the repeated arithmetic means of,, generated regularly by a sequence in the class, is also a subsequential convergence condition for.

Tauberian conditions under which convergence follows from Abel summability

Abstract In this work we prove that one-sided slow oscillation of a sequence and that of its generator sequence are Tauberian conditions for the Abel summability method, using a corollary to Karamata’s Main Theorem [J. Karamata, Uber die Hardy–Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes, Math. Z. 32 (1930) 319–320]. It is also shown that such conditions are Tauberian conditions for generalized Abelian summability methods.

Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers

Abstract In this paper, we prove that a bounded double sequence of fuzzy numbers which is statistically convergent is also statistically (C, 1, 1) summable to the same number. We construct an example that the converse of this statement is not true in general. We obtain that the statistically (C, 1, 1) summable double sequence of fuzzy numbers is convergent and statistically convergent to the same number under the slowly oscillating and statistically slowly oscillating conditions in certain senses, respectively.

Some Tauberian theorems for the product method of Borel and Cesàro summability

In this paper we prove several new Tauberian theorems for the product of Borel and Cesaro summability methods which improve classical Tauberian theorems for the Borel summability method.