Tauberian theorems for subsequential convergence

Bu tezde iyi bilinen bazı toplanabilme metotları, düzenli üretilen diziler ve yakınsak dizilerin sınıfını içeren bazı dizi sınıfları için Tauber tipi teoremler verilmiştir. Bu teoremlerde verilen koşullarda dizinin salınım davranışlarının genel kontrol modülosu, yavaş salınımlılığı ve ılımlı salınımlılığı gibi kavramlar kullanılarak o dizinin altdizisel yakınsaklığı elde edilmiştir. Ayrıca altdizisel yakınsaklığın elde edildiği teoremlerin genelleştirilmelerine yer verilmiştir. Birinci bölümde teze giriş yapılmıştır. İkinci bölümde tez boyunca kullanılacak tanımlamalar ve gösterimler verilmiştir ve Tauber teorisinden bahsedilmiştir. Üçüncü bölümde altdizisel yakınsaklık kavramından kapsamlı olarak bahsedilmiştir ve altdizisel yakınsaklığın elde edildiği Tauber tipi teoremler verilmiştir. Dördüncü bölümde düzenli üretilen dizi kavramı ve bu dizilerin altdizisel yakınsaklıklarının elde edildiği Tauber tipi teoremler verilmiştir. In this thesis, some well-known summability methods, regular generated sequences and Tauberian theorems for some classes of sequence which contain the class of convergent sequences are given. On the conditions that are given in this theorems, subsequential convergence of a sequence is obtained by using concepts like general control modulo of oscillatory behaviors of the sequence, slow oscilation of the sequence and moderate oscilation of the sequence. Also generalizations of theorems, from which subsequential convergence is obtained, are given. In the first chapter, introduction is done to thesis. In the second chapter, all the definitions and notations used in the thesis are given, and Tauberian theory is mentioned. In the third chapter, the concept of subsequential convergent is mentioned comprehensively, and Tauberian theorems, from which subsequential convergence is obtained, are given. In the fourth chapter, the concept of regular generated sequence is given, and Tauberian theorems, from which subsequential convergence of these sequences is obtained, are given

Some Tauberian Remainder Theorems for Holder Summability

In this paper, we prove some Tauberian remainder theorems that generalize the results given by Meronen and Tammeraid [Math. Model. Anal., 18(1):97– 102, 2013] for Holder summability method using the notion of the general control modulo of the oscillatory behaviour of nonnegative integer order

ONE-SIDED TAUBERIAN CONDITIONS FOR THE ((N)over-bar, p) SUMMABILITY OF INTEGRALS

WOS: 000441473800007Let p be a function on R+ := [0, infinity) which is integrable in Lebesgue's sense over every finite interval (0; x) for 0 0, P (0) = 0 and P (x) -> infinity as x -> infinity. For a real-valued function f is an element of L-loc(1) (R+), we set s (x) := integral(0)(x) f (t)dt and sigma((1))(p) (x) := 1/P(x) integral(x)(0) s (t) p (t)dt; x > 0, provided that P (x) > 0. We say that integral(infinity)(0) f (x) dx is summable by the weighted mean method determined by the function P (x) if there exists some s is an element of R such that lim(x ->infinity) sigma((1))(p) (x) = 8. If the limit lim(x -> infinity) s (x) = s exists, then so does lim(x ->infinity) sigma((1))(p) (x) = s. In this paper, we obtain some new Tauberian conditions in terms of the weighted general control modulo for the weighted mean method of integrals in order that the converse implication hold true. Our results generalize some classical type Tauberian theorems given for Cesaro summability method of integrals