İbrahim Çanak

New Types of Continuities

A new concept of quasi slowly oscillating continuity is introduced. Furthermore, it is shown that this kind of continuity implies ordinary continuity, but the converse is not always true.

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).

On the Riesz mean of sequences of fuzzy real numbers

We state and prove a fuzzy analogue of a Theorem due to Moricz and Rhoades [Acta Math. Hungar. 102 (4) (2004), 279–285].

On Tauberian theorems for Cesàro summability of sequences of fuzzy numbers

In this paper we use the concept of the Cesaro convergence of a sequence of fuzzy numbers defined by Subrahmanyam [Cesaro summability of fuzzy real numbers, Anal, 7 (1999), 159–168] to prove some Tauberian theorems for sequences of fuzzy numbers and obtain fuzzy analogues of some classical Tauberian theorems for Cesaro summability of sequences of fuzzy numbers as a corollary.

Some Tauberian theorems for the weighted mean methods of summability

In this paper, we introduce the concept of the weighted generator sequence and prove that certain conditions in terms of weighted generator sequences are Tauberian conditions for the weighted mean summability method.

Some general Tauberian conditions for the weighted mean summability method

In this paper, we obtain some new Tauberian theorems for the weighted mean summability method via a weighted general control modulo analogous to the one defined by Dik [M. Dik, Tauberian theorems for sequences with moderately oscillatory control moduli, Math. Morav. 5 (2001) 57-94].

A Tauberian theorem for the weighted mean method of summability of sequences of fuzzy numbers

In this paper, a Tauberian theorem of slowly decreasing type is proved for the weighted mean method of summability of sequences of fuzzy numbers.

Tauberian conditions for Cesaro summability of integrals

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

Some Tauberian theorems for (A)(C ,α) summability method

In this paper we give some Tauberian conditions in order to obtain (C,@a) summability from (A)(C,@a) summability.

A condition under which slow oscillation of a sequence follows from Cesàro summability of its generator sequence

In this paper we retrieve slow oscillation of a real sequence from Cesaro summability of its generator sequence under some one-sided condition.