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

Gökşen Fındık; İbrahim Çanak

doi:10.5269/bspm.v38i7.44135

Gökşen Fındık Ege University http://orcid.org/0000-0002-2356-3987
İbrahim Çanak Ege University http://orcid.org/0000-0002-1754-1685

DOI: https://doi.org/10.5269/bspm.v38i7.44135

Abstract

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.

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Author Biography

İbrahim Çanak, Ege University

Ibrahim Canak is Professor of Mathematics at Ege University, Izmir, Turkey. He was born in Tokat, Turkey on October 1, 1967. He received his primary and secondary education in Istanbul, Turkey. He received his B.S. degree in 1988 with the highest rank in Mathematics from University of Istanbul, Istanbul, Turkey. October 1988 through October 1992 he was a graduate student and teaching assistant. While he was a graduate teaching assistant at University of Istanbul in 1993, he won a scholarship from the Higher Education Council of Turkey to get Ph.D. degree in the USA. He received his doctoral degree in 1998 under the direction of Professor Dr. Caslav V. Stanojevic at the University of Missouri – Rolla, Missouri, USA. He joined Adnan Menderes University, Aydin, Turkey in the fall of 1993 as a research assistant. He is the author of over 60 research papers. His current area of research and interest is summability theory. He is a member of American Mathematical Society and Mathematical Association of Turkey. He has been on the faculty of Ege University since 2010. He has been a referee and/or reviewer for several journals, MathSciNet and Zentrallblatt-Math and is also on the editorial board of several mathematics journals.

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