Abstract
In this paper, we obtain necessary and sufficient conditions for the equivalence of two matrix summability methods. Some known results are also presented.
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References
W. T. Sulaiman, “Inclusion theorems for absolute matrix summability methods of an infinite series. IV,” Indian J. Pure Appl. Math. 34 (11), 1547–1557 (2003).
H. S. Özarslan and H. N. Öǧdük, “Generalizations of two theorems on absolute summability methods,” Aust. J. Math. Anal. Appl. 1 (2) (2004) Article 13.
N. Tanovic-Miller, “On strong summability,” Glas. Mat., III. Ser. 14 (34), 87–97 (1979).
H. Bor, “On two summability methods,” Math. Proc. Camb. Philos. Soc. 97, 147–149 (1985).
R. G. Cooke, Infinite Matrices and Sequence Spaces (Macmillan & C., Ltd., London, 1950).
H. Bor, “A note on two summability methods,” Proc. Am. Math. Soc. 98 (1), 81–84 (1986).
H. Bor and B. Kuttner, “On the necessary conditions for absolute weighted arithmetic mean summability factors,” Acta Math. Hung. 54 (1–2), 57–61 (1989).
H. Bor, “On the relative strength of two absolute summability methods,” Proc. Am. Math. Soc. 113 (4), 1009–1012 (1991).
H. Bor and B. Thorpe, “A note on two absolute summability methods,” Analysis 12, 1–3 (1992).
H. Bor, “Some equivalence theorems on absolute summability methods,” Acta. Math. Hung. 149, 208–214 (2016).
H. Bor, “On absolute summability of factored infinite series and trigonometric Fourier series,” Result. Math. 73 (2018) Paper No. 116.
H. Bor, “Certain new factor theorems for infinite series and trigonometric Fourier series,” Quaest. Math. 43 (4), 441–448 (2020).
H. Bor, “Factored infinite series and Fourier series involving almost increasing sequences,” Bull. Sci. Math. 169 (2021) Article ID 102990.
H. Bor, “Absolute weighted arithmetic mean summability of factored infinite series and Fourier series,” Bull. Sci. Math. 176 (2022) Article ID 103116.
H. Bor, “On absolute weighted arithmetic mean summability of infinite series and Fourier series,” Proc. Am. Math. Soc. 150 (8), 3517–3522 (2022).
H. S. Özarslan, “A new application of absolute matrix summability,” C. R. Acad. Bulg. Sci. 68 (8), 967–972 (2015).
H. S. Özarslan and H. N. Özgen, “Necessary conditions for absolute matrix summability methods,” Boll. Unione Mat. Ital. 8 (3), 223–228 (2015).
H. S. Özarslan and B. Kartal, “Absolute matrix summability via almost increasing sequence,” Quaest. Math. 43 (10), 1477–1485 (2020).
H. N. Özgen, “A note on generalized absolute summability,” An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 59 (1), 185–190 (2013).
H. N. Özgen, “On two absolute matrix summability methods,” Boll. Unione Mat. Ital. 9 (3), 391–397 (2016).
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The author expresses her thanks to the referee for his/her comments for the improvement of this paper.
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Özgen, H.N. Equivalence Theorem for Absolute Matrix Summability Methods. Math Notes 114, 1322–1327 (2023). https://doi.org/10.1134/S0001434623110640
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DOI: https://doi.org/10.1134/S0001434623110640