Double uniform density and corresponding convergence of double sequences

Pratulananda Das; Ekrem Savas

doi:10.1556/sscmath.49.2012.4.1208

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 49: Issue 4

Double uniform density and corresponding convergence of double sequences

Authors:

Pratulananda Das

Pratulananda Das Jadavpur University Department of Mathematics Kolkata 700032 West Bengal India

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Ekrem Savas

Ekrem Savas Istanbul Ticaret University Department of Mathematics Üsküdar-Istanbul Turkey

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Pages:: 419–435

Online Publication Date:: 16 Nov 2012

Publication Date:: 01 Dec 2012

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.49.2012.4.1208

Keywords:: Primary 40A05; Secondary 11C05; double uniform density; almost convergence; uniformly strong p-Cesàro convergence; double sequences; four dimensional matrices; matrix transformation.

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We introduce the concept of double uniform density of subsets of ℕ×ℕ and the study the corresponding convergence (namely, I_u-convergence) of double sequences. Further we solve an inequality related to the I_u-limit superior of bounded double sequences in line of [5].

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

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András STIPSICZ (Rényi Institute of Mathematics)
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Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
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Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
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Frédéric MEUNIER (École des Ponts ParisTech)
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János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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