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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

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2017: 0.23

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1572-9176
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General Tauberian theorems for the Cesàro integrability of functions

Ümit Totur / İbrahim ÇanakORCID iD: https://orcid.org/0000-0002-1754-1685
Published Online: 2019-02-15 | DOI: https://doi.org/10.1515/gmj-2019-2005

Abstract

For a locally integrable function f on [0,), we define

F(t)=0tf(u)duandσα(t)=0t(1-ut)αf(u)du

for t>0. The improper integral 0f(u)du is said to be (C,α) integrable to L for some α>-1 if the limit limxσα(t)=L exists. It is known that limtF(t)= implies limtσα(t)= for α>-1, but the converse of this implication is not true in general. In this paper, we introduce the concept of the general control modulo of non-integer order for functions and obtain some Tauberian conditions in terms of this concept for the (C,α) integrability method in order that the converse implication hold true. Our results extend the main theorems in [Ü. Totur and İ. Çanak, Tauberian conditions for the (C,α) integrability of functions, Positivity 21 2017, 1, 73–83].

Keywords: Cesàro integrability; one-sided Tauberian condition; slow decreasing; Tauberian theorem and condition

MSC 2010: 40A10; 40AC10; 40D05

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About the article

Received: 2016-08-11

Revised: 2017-05-22

Accepted: 2017-06-28

Published Online: 2019-02-15


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2005.

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