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.

Classical Tauberian Theorems for the (C; 1; 1) Summability Method

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Ümit Totur
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Subject Classification ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Littlewood Theorem

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0

scholarly journals Results on Tauberian Theorem for Cesàro Summable Double Sequences of Fuzzy Numbers

2020 ◽  
Vol 44 (4) ◽  
pp. 495-508 ◽  
Author(s):  
B. B. Jena ◽  
S. K. PAIKRAY ◽  
P. PARIDA ◽  
H. DUTTA
Keyword(s):  
Tauberian Theorem ◽  
Fuzzy Numbers ◽  
Double Sequences ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Special Cases ◽  
Sequences Of Fuzzy Numbers

The paper aims to establish new results on Tauberian theorem for Cesàro summability of double sequences of fuzzy numbers, and thus to extend and unify several results in the available literature. Further, a number of special cases, corollaries and illustrative example in support of the investigation of this paper are also presented.

scholarly journals Statistical Tauberian theorems for Cesàro integrability mean based on post-quantum calculus

2020 ◽  
Vol 9 (3) ◽  
pp. 653-663
Author(s):  
P. Parida ◽  
S. K. Paikray ◽  
B. B. Jena
Keyword(s):  
Continuous Function ◽  
Statistical Convergence ◽  
Tauberian Theorems ◽  
Cesàro Summability ◽  
Quantum Calculus ◽  
Cesaro Summability ◽  
Single Integral ◽  
De La Vallée Poussin

Abstract The notion of statistical convergence is more general than the classical convergence. Tauberian theorems via different ordinary summability means have been established by many researchers. In the present work, we have established some new Tauberian theorems based on post-quantum calculus via statistical Cesàro summability mean of real-valued continuous function of one variable under oscillating behavior and De la vallée Poussin mean of a single integral. Moreover, some remarks and corollaries are provided here to support our theorems.

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 Tauberian theorems for Cesàro summability of nth sequences

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3993-4004 ◽  
Author(s):  
P. Parida ◽  
S.K. Paikray ◽  
Hemen Dutta ◽  
B.B. Jena ◽  
M. Dash
Keyword(s):  
Tauberian Theorem ◽  
Slow Oscillation ◽  
Tauberian Theorems ◽  
Cesàro Summability ◽  
Cesaro Summability

Tauberian theorem provides a criterion for the convergence of non convergent (summable) sequences. In this paper, we established a Tauberian theorem for nth real sequences via Ces?ro summability by using de la Vall?e Poussin mean and slow oscillation. The discussion and findings are capable to unify several useful concepts in the literature, and should also provide nontrivial extension of several results. Some examples are incorporated in support of our definitions and results. The findings are further expected to be helpful in designing and study several other interesting problems in summability theory and applications.

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.

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.

Some sequence spaces and completeness of normed spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 281-287
Author(s):  
RAMAZAN KAMA ◽  
◽  
BILAL ALTAY ◽  
Keyword(s):  
Normed Space ◽  
Summability Method ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Cesàro Summability ◽  
Cesaro Summability

In this paper we introduce new sequence spaces obtained by series in normed spaces and Cesaro summability method. We prove that completeness ´ and barrelledness of a normed space can be characterized by means of these sequence spaces. Also we establish some inclusion relationships associated with the aforementioned sequence spaces.

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