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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

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1572-9176
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A Tauberian theorem for the generalized Nörlund summability method

İbrahim ÇanakORCID iD: http://orcid.org/0000-0002-1754-1685 / Naim L. Braha
  • Department of Computer Sciences and Applied Mathematics, College Vizioni per Arsim, Rr, Ahmet Kaciku, Ferizaj, 70000, Kosovo
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/ Ümit ToturORCID iD: http://orcid.org/0000-0001-8114-0539
Published Online: 2018-01-10 | DOI: https://doi.org/10.1515/gmj-2017-0062

Abstract

Let (pn) and (qn) be any two non-negative real sequences, with Rn:=k=0npkqn-k0 (n). Let k=0ak be a series of real or complex numbers with partial sums (sn), and set tnp,q:=1Rnk=0npkqn-ksk for n. In this paper, we present the necessary and sufficient conditions under which the existence of the limit limnsn=L follows from that of limntnp,q=L. These conditions are one-sided or two-sided if (sn) is a sequence of real or complex numbers, respectively.

Keywords: Generalized Nörlund summability; one-sided and two-sided Tauberian conditions

MSC 2010: 40G15; 41A36

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About the article

Received: 2015-07-16

Accepted: 2016-05-23

Published Online: 2018-01-10


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2017-0062.

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