Zerrin ÖnderÖnder, Zerrin2025-10-222025Ishiguro K. On the summability methods of logarithmic type Proceedings of the Japan Academy 38 703-705 (1962).Ishiguro K. A converse theorem on the summability methods Proceedings of the Japan Academy 39 38-41 (1963).Hardy G. H. Divergent Series Clarendon Press Oxford (1949).Szász O. Introduction to the theory of divergent series University of Cincinnati Ohio (1952).Ishiguro K. Tauberian theorems concerning the summability method of logarithmic type Proceedings of the Japan Academy 39 156-159 (1963).Ishiguro K. A note on the logarithmic means Proceedings of the Japan Academy 39 575-577 (1963).Kwee B. A Tauberian theorem for the logarithmic method of summation Proceedings of the Cambridge Philosophical Society 63 401-405 (1966).Kwee B. Some Tauberian theorems for the logarithmic method of summability Canadian Journal of Mathematics 20 1324-1331 (1968).Kwee B. On generalized logarithmic methods of summation Journal of Mathematical Analysis and Applications 35 83-89 (1971).Rangachari M. S. and Sitaraman Y. Tauberian theorems for logarithmic summability (L) The Tohoku Mathematical Journal (2) 16 257-269 (1964).Kaufman B. L. Theorems of Tauberian type for logarithmic methods of summation Izvestija Vysših Učebnyh Zavedeniĭ Matematika 1 56 57-62 (1967).Kohanovskiĭ A. P. Theorems of Tauberian type for a semicontinuous logarithmic method of summability of series Ukrainskiĭ Matematičeskiĭ Žurnal 26 740-748 861 (1974).Kohanovskiĭ A. P. A condition for the equivalence of logarithmic summability methods Ukrainskiĭ Matematičeskiĭ Žurnal 27 229-234 285 (1975).Burljai M. F. The logarithmic method for the summability of numerical double series Izvestija Vysših Učebnyh Zavedeniĭ Matematika 3 166 95-98 (1976).Móricz F. Theorems relating to statistical harmonic summability and ordinary convergence of slowly decreasing or oscillating sequences Analysis 24 2 127-145 (2004).Móricz F. Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences Studia Mathematica 219 2 109-121 (2013).Alghamdi M. A. Mursaleen M. and Alotaibi A. Logarithmic density and logarithmic statistical convergence Advances in Difference Equations 2013:227 6 (2013).Totur Ü. and Okur M. A. On logarithmic averages of sequences and its applications Kuwait Journal of Science 43 4 56-67 (2016).Sezer S. A. and Çanak İ. Tauberian theorems for the summability methods of logarithmic type Bulletin of the Malaysian Mathematical Sciences Society 41 4 1977-1994 (2018).Sezer S. A. and Çanak İ. Tauberian conditions of slowly decreasing type for the logarithmic power series method Proceedings of the National Academy of Sciences India Section A: Physical Sciences 90 1 135-139 (2020).Çınar N. and Çanak İ. Necessary and sufficient Tauberian conditions under which statistically logarithmic convergence follows from statistically logarithmic summability Journal of Classical Analysis 21 1 29-34 (2023).Okur M. A. General logarithmic control modulo and Tauberian remainder theorems Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 73 2 391-398 (2024).Maddox I. J. A Tauberian theorem for ordered spaces Analysis 9 3 297-302 (1989).Çanak I. A Tauberian theorem for a weighted mean method of summability in ordered spaces National Academy Science Letters 43 6 553–555 (2020).Pringsheim A. Zur Theorie der zweifach unendlichen Zahlenfolgen Mathematische Annalen 53 3 289-321 (1900).Tauber A. Ein Satz aus der Theorie der unendlichen Reihen Monatshefte für Mathematik und Physik 8 1 273-277 (1897).Knopp K. Limitierungs-Umkehrsätze für Doppelfolgen Mathematische Zeitschrift 45 573-589 (1939).Totur Ü. Classical Tauberian theorems for the (C 1 1) summability method Analele Ştiinţifice ale Universităţii “Alexandru Ioan Cuza” din Iaşi Serie Nouă Matematică 61 2 401-414 (2015).Schmidt R. Über divergente Folgen und lineare Mittelbildungen Mathematische Zeitschrift 22 1 89-152 (1925).1301-79852536-514210.25092/baunfbed.1556267https://gcris.yasar.edu.tr/handle/123456789/10417https://search.trdizin.gov.tr/en/yayin/detay/1298500Bu çalışma daha önce sıralı uzaylardaki tek katlı dizilerin Cesàro ve ağırlıklı ortalama toplanabilirlik yöntemleri için oluşturulmuş Tauber tipi teoremleri iki katlı diziler için logaritmik toplanabilirlik yöntemine diğer adıyla (ℓ 1 1) yöntemine genişletmeyi amaçlar. Bu amaçla çeşitli anlamlarda logaritmik toplanabilirliğe göre iki katlı bir (s_mn ) dizinin O_L-salınım davranışını ele alan birkaç Tauber tipi koşul sunuyoruz. Bu koşullar sıralı uzaylarda dizinin (ℓ 1 1) (ℓ 1 0) ve (ℓ 0 1) toplanabilirliğinden P-yakınsaklığına geçişine olanak sağlar.İngilizceinfo:eu-repo/semantics/openAccessMatematikArticle