scholarly journals Tauberian theorems for the product of weighted and Cesàro summability methods of double sequences

2019 ◽  
Author(s):  
Gökşen Fındık ◽  
İbrahim Çanak
Keyword(s):  
Tauberian Theorems ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Summability Methods ◽  
Cesaro Summability

scholarly journals Tauberian Theorems for the Product of Weighted and Cesàro Summability Methods for Double Sequences

2019 ◽  
Vol 38 (7) ◽  
pp. 9-19
Author(s):  
Gökşen Fındık ◽  
İbrahim Çanak
Keyword(s):  
Double Sequence ◽  
Sufficient Conditions ◽  
Complex Numbers ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Tauberian Conditions ◽  
Summability Methods ◽  
Cesaro Summability ◽  
Necessary And Sufficient

In this paper, we obtain necessary and sufficient conditions, under which convergence of a double sequence in Pringsheim's sense follows from its weighted-Cesaro summability. These Tauberian conditions are one-sided or two-sided if it is a sequence of real or complex numbers, respectively.

scholarly journals Convergence follows from Cesàro summability in the case of slowly decreasing or slowly oscillating double sequences in certain senses

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4489-4511
Author(s):  
Zerrin Önder ◽  
İbrahim Çanak
Keyword(s):  
Double Sequence ◽  
Complex Numbers ◽  
Tauberian Theorems ◽  
Finite Limit ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Tauberian Conditions ◽  
Summability Methods ◽  
Cesaro Summability ◽  
Special Cases

Let (u??) be a double sequence of real or complex numbers which is (C; 1; 1) summable to a finite limit. We obtain some Tauberian conditions of slow decreasing or oscillating types in terms of the generator sequences in certain senses under which P-convergence of a double sequence (u??) follows from its (C,1,1) summability. We give Tauberian theorems in which Tauberian conditions are of Hardy and Landau types as special cases of our results. We present some Tauberian conditions in terms of the de la Vall?e Poussin means of double sequences under which P-convergence of a double sequence (u??) follows from its (C,1,1) summability. Moreover, we give analogous results for (C,1,0) and (C,0,1) summability methods.

scholarly journals A Tauberian Theorem for Double Cesàro Summability Method

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
Bidu Bhusan Jena ◽  
Susanta Kumar Paikray ◽  
Umakanta Misra
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
De La Vallée Poussin

We have generalized Littlewood Tauberian theorems for(C,k,r)summability of double sequences by using oscillating behavior and de la Vallée-Poussin mean. Further, the generalization of(C,r)summability from(C,k,r)summability is given as corollaries which were earlier established by the authors.

A Tauberian theorem for the product of Abel and Cesàro summability methods

2016 ◽  
Vol 23 (3) ◽  
pp. 343-350 ◽  
Author(s):  
Yılmaz Erdem ◽  
İbrahi̇m Çanak
Keyword(s):  
Tauberian Theorem ◽  
Tauberian Theorems ◽  
Cesàro Summability ◽  
Summability Methods ◽  
Cesaro Summability ◽  
Cesàro Method

AbstractIn this paper, we prove a Tauberian theorem for the product of the Abel method and the Cesàro method of order α, which improves some classical Tauberian theorems for the Abel and Cesàro summability methods.

Deferred Cesàro summability and statistical convergence for double sequences of sets

2021 ◽  
pp. 1-9
Author(s):  
Uğur Ulusu ◽  
Esra Gülle
Keyword(s):  
Statistical Convergence ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Cesàro Mean ◽  
Cesaro Summability ◽  
Cesaro Mean

The main purpose of this paper is introduced the concept of deferred Cesàro mean in the Wijsman sense for double sequences of sets and then presented the concepts of strongly deferred Cesàro summability and deferred statistical convergence in the Wijsman sense for double sequences of sets. Also, investigate the relationships between these concepts and then to prove some theorems associated with the concepts of deferred statistical convergence in the Wijsman sense for double sequences of sets is purposed.

scholarly journals Tauberian conditions under which convergence follows from Cesàro summability of double integrals over R2

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3425-3440
Author(s):  
Gökşen Fındık ◽  
İbrahim Çanak
Keyword(s):  
Continuous Function ◽  
The Other ◽  
Cesàro Summability ◽  
Double Integral ◽  
Tauberian Conditions ◽  
Summability Methods ◽  
Cesaro Summability ◽  
The Difference ◽  
Complex Valued ◽  
Double Integrals

For a real- or complex-valued continuous function f over R2+:= [0,1) x [0,1), we denote its integral over [0,u] x [0,v] by s(u,v) and its (C,1, 1) mean, the average of s(u,v) over [0,u] x [0,v], by ?(u,v). The other means (C,1,0) and (C; 0; 1) are defined analogously. We introduce the concepts of backward differences and the Kronecker identities in different senses for double integrals over R2+. We give onesided and two-sided Tauberian conditions based on the difference between double integral of s(u, v) and its means in different senses for Ces?ro summability methods of double integrals over [0,u] x [0,v] under which convergence of s(u,v) follows from integrability of s(u,v) in different senses.

Summability methods which include the Riesz typical means. I

1971 ◽  
Vol 69 (1) ◽  
pp. 99-106 ◽  
Author(s):  
Dennis C. Russell
Keyword(s):  
Complete Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Alternative Form ◽  
Cesàro Summability ◽  
Abel Summability ◽  
Summability Methods ◽  
Cesaro Summability ◽  
Riesz Summability ◽  
Necessary And Sufficient

A number of special results exist for summability methods B which, include Riesz summability (R,λ,k)—for example, when B is generalized Abel summability (A,λ,ρ) [Kuttner(5)], or Riemann summability (,λ,μ) [Russell(14)], or Riemann-Cesàro summability (,λ,p,α) [Rangachari(12)], or generalized Cesàro summability (C,λ,k) [Meir (9); Borwein and Russell (l)]. The question of necessary and sufficient conditions to be satisfied by an arbitrary method B in order that B ⊇ (R,λ,k) has received an answer only for limited values of λ and k—for example, by Lorentz [(6), Theorem 10] for k = 1; the restrictions on λ in this case were removed by Maddox [(8), Theorem 1]. Thus (apart from the well-known case k = 0) the case k = 1 is the only one for which a complete solution exists, though application of a theorem of Russell [(13), Theorem 1A] yields one form of a result for 0 < k ≤ 1. Maddox's results, however, suggest an alternative form capable of generalization to all k ≥ 0, and in this paper we obtain a complete solution for 0 < k ≤ 1 in that form, without restriction on λ. We first recall the following definitions.

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