Browsing by Author "Çanak, İbrahim"
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DeltaQuasislowly oscillating continuity
Çakallı, Hüseyin; Çanak, İbrahim; Dik, Mehmet (ScienceDirect, 2016)Firstly, some definitions and notations will be given in the following. Throughout this paper, N will denote the set of all positive integers. We will use boldface letters x,y,z,. . . for sequences x = (xn),y = (yn),z= ... 
Logarithmic summability (L, 1) of integrals on [1, ∞)
Fındık, Gökşen; Çanak, İbrahim (Maltepe Üniversitesi, 2019)Móricz [3] characterized summability (C, 1) of integrals by convergence of another integral. In this work, we extend this result to logarithmic summability (L, 1) of integrals. 
Logarithmic summability of integrals on [1,∞)
Fındık, Gökşen; Çanak, İbrahim (Maltepe Üniversitesi, 2019)Moricz [2] characterized (C, 1) summability of integrals by convergence of another integral. In this work, we extend this result to logarithmic summability (L, 1) of integrals. 
Necessary and sufficient tauberian conditions under which convergence follows from Ar,δ summability
Kambak, Çağla; Çanak, İbrahim (Maltepe Üniversitesi, 2019)We say that (xmn) is (A r,δ , 1, 1) summable to l if the sequence (σ r,δ mn(x)) has a finite limit l. It is known that if limm,n→∞ xmn = l and (xmn) is bounded, then the limit limm,n→∞ σ r,δ mn(x) = l exists. But ... 
On tauberian theorems for (A, k) summability method
Çanak, İbrahim; Totur, Ümit; Dik, Mehmet (Maltepe Üniversitesi, 2009)Let (un) be a sequence of real numbers which is (A, k) summable. In this work, several new Tauberian theorems for (A, k) summability methods will be given in terms of generating sequences of (un). 
A revisited Tauberian theorem for which slow decrease with respect to a weight function is a tauberian condition for the weighted mean summability of integrals over R+
Çanak, İbrahim (Maltepe Üniversitesi, 2021). In this extended abstract, we present an alternative proof of a Tauberian theorem of slowly decreasing type with respect to the weight function due to Karamata [5] for the weighted mean summable realvalued integrals ... 
Some tauberian theorems for (C, 1, 1) summability method by regularly generated integrals
Fındık, Gökşen; Çanak, İbrahim (Maltepe Üniversitesi, 2019)We introduce the concept of regularly generated integrals for improper double integrals. We prove several Tauberian theorems for the (C, 1, 1) summability method of improper double integrals by using regularly generated ... 
Some tauberian theorems for borel summability methods
Çanak, İbrahim; Totur, Ümit (Maltepe Üniversitesi, 2009)We investigate the conditions needed for a Borel summable sequence to be convergent. The results of this paper extend and improve the well known result of Hardy and Littlewood [Proc. London Math. Soc. 11 (1913), 116]. 
Some tauberian theorems for weighted means of double integrals on R2+
Fındık, Gökşen; Çanak, İbrahim (Maltepe Üniversitesi, 2019)Let p(x) and q(y) be nondecreasing continuous functions on [0, ∞) such that p(0) = q(0) = 0 and p(x), q(y) → ∞ as x, y → ∞. For a locally integrable function f(x, y) on R 2 + = [0, ∞) × [0, ∞), we denote its double ... 
Statistical extensions of Tauberian theorems for the weighted mean method of summability in twonormed spaces
Bakıcıerler, Hülya; Çanak, İbrahim (Maltepe Üniversitesi, 2021)In this extended abstract, we first define the concept of statistical summability (N, p) in 2normed spaces and then present necessary and/or sufficient Tauberian conditions for statistical summability (N, p) in 2normed spaces. 
Sufficient tauberian conditions for the (N, p) summability of sequences
Sezer, Sefa Anıl; Çanak, İbrahim (Maltepe Üniversitesi, 2019)It is known that limn→∞ un = s implies limn→∞ σ (1) n,p(u) = s if and only if (1) is satisfied. However, the converse is not true in general. In this paper our aim is to find conditions under which the converse ... 
Tauberian theorems for (A)(C, α) summability method
Çanak, İbrahim; Erdem, Yılmaz; Totur, Ümit (Maltepe Üniversitesi, 2009)Using Tauberian theorems for Abel summability method by Hardy [1], Littlewood [2] and Pati [3], we have given several Tauberian theorems for (A)(C, α) summability method. Also in this work some theorems given by Pati [3] ... 
Tauberian theorems for the product of weighted and cesaro summability methods of double sequences
Fındık, Gökşen; Çanak, İbrahim (Maltepe Üniversitesi, 2019)A double sequence u = (umn) is called convergent in Pringsheim’s sense (in short Pconvergent) to s [? ], if for a given ε > 0 there exists a positive integer N0 such that umn − s < ε for all nonnegative integers m, n ... 
Tauberian theorems for the weighted mean summability of integrals on [1, ∞)
Çanak, İbrahim; Özsanaç, Fırat (Maltepe Üniversitesi, 2019)In this work, we obtain some Tauberian theorems for the weighted mean method of integrals on [1, ∞). As special cases, we give some Tauberian theorems for Ces`aro summability of integrals on [1, ∞). 
Theorems on the subsequential convergence
Sezer, Sefa Anıl; Çanak, İbrahim (Maltepe Üniversitesi, 2019)In this study we obtain some sufficient conditions under which subsequential convergence of a sequence of real numbers follows from its boundedness. Eventually, we obtain crucial information about the subsequential behavior ...