In
this paper, a theorem on absolute summability of infinite series is obtained by
taking almost increasing sequence instead of positive non-decreasing sequence.
Also, some results of absolute summability are given.
[1] Bari N.K. and Stečkin S.B., Best Approximations and Differential Properties of Two Conjugate Functions, Trudy Moskov. Mat. Obšč., 5 (1956) 483-522.
[2] Seyhan H., On the Local Property of Summability of Factored Fourier Series, Bull. Inst. Math. Acad. Sinica, 25-4 (1997) 311-316.
[3] Hardy G.H., Divergent Series, Oxford, Oxford University Press, 1949.
[4] Bor H., On Local Property of Summability of Factored Fourier Series, J. Math. Anal. Appl., 179-2 (1993) 646-649.
[5] Bor H., On Two Summability Methods, Math. Proc. Cambridge Philos. Soc., 97-1 (1985) 147-149.
[6] Flett T.M., On an Extension of Absolute Summability and Some Theorems of Littlewood and Paley, Proc. London Math. Soc. (3), 7 (1957) 113-141.
[7] Bor H., A Note on Absolute Summability Factors, Internat. J. Math. Math. Sci., 17-3 (1994) 479-482.
[8] Bor H. and Seyhan H., On Almost Increasing Sequences and Its Applications, Indian J. Pure Appl. Math., 30-10 (1999) 1041-1046.
[9] Bor H. and Özarslan H.S., On Absolute Riesz Summability Factors, J. Math. Anal. Appl., 246-2 (2000) 657-663.
[10] Bor H. and Özarslan H.S., An Application of Quasi Power Increasing Sequences, Int. Math. J., 2-2 (2002) 187–191.
[11] Bor H. and Özarslan H.S., On an Application of Quasi Power Increasing Sequences, Indian J. Pure Appl. Math., 33-5 (2002), 769–774.
[12] Bor H. and Özarslan H.S., A Note on Absolute Summability Factors, Adv. Stud. Contemp. Math. (Kyungshang) 6-1 (2003) 1-11.
[13] Bor H. and Özarslan H.S., A Note on Absolute Weighted Mean Summability Factors, Cent. Eur. J. Math., 4-4 (2006) 594–599.
[14] Karakaş A., A Note on Absolute Summability Method Involving Almost Increasing and -quasi-monotone sequences, Int. J. Math. Comput. Sci., 13-1 (2018) 73-81.
Bu makalede,
pozitif azalmayan dizi yerine hemen hemen artan dizi alınarak, sonsuz
serilerin mutlak toplanabilmesi üzerine bir teorem elde edildi. Ayrıca, mutlak
toplanabilme ile ilgili bazı sonuçlar
verildi.
[1] Bari N.K. and Stečkin S.B., Best Approximations and Differential Properties of Two Conjugate Functions, Trudy Moskov. Mat. Obšč., 5 (1956) 483-522.
[2] Seyhan H., On the Local Property of Summability of Factored Fourier Series, Bull. Inst. Math. Acad. Sinica, 25-4 (1997) 311-316.
[3] Hardy G.H., Divergent Series, Oxford, Oxford University Press, 1949.
[4] Bor H., On Local Property of Summability of Factored Fourier Series, J. Math. Anal. Appl., 179-2 (1993) 646-649.
[5] Bor H., On Two Summability Methods, Math. Proc. Cambridge Philos. Soc., 97-1 (1985) 147-149.
[6] Flett T.M., On an Extension of Absolute Summability and Some Theorems of Littlewood and Paley, Proc. London Math. Soc. (3), 7 (1957) 113-141.
[7] Bor H., A Note on Absolute Summability Factors, Internat. J. Math. Math. Sci., 17-3 (1994) 479-482.
[8] Bor H. and Seyhan H., On Almost Increasing Sequences and Its Applications, Indian J. Pure Appl. Math., 30-10 (1999) 1041-1046.
[9] Bor H. and Özarslan H.S., On Absolute Riesz Summability Factors, J. Math. Anal. Appl., 246-2 (2000) 657-663.
[10] Bor H. and Özarslan H.S., An Application of Quasi Power Increasing Sequences, Int. Math. J., 2-2 (2002) 187–191.
[11] Bor H. and Özarslan H.S., On an Application of Quasi Power Increasing Sequences, Indian J. Pure Appl. Math., 33-5 (2002), 769–774.
[12] Bor H. and Özarslan H.S., A Note on Absolute Summability Factors, Adv. Stud. Contemp. Math. (Kyungshang) 6-1 (2003) 1-11.
[13] Bor H. and Özarslan H.S., A Note on Absolute Weighted Mean Summability Factors, Cent. Eur. J. Math., 4-4 (2006) 594–599.
[14] Karakaş A., A Note on Absolute Summability Method Involving Almost Increasing and -quasi-monotone sequences, Int. J. Math. Comput. Sci., 13-1 (2018) 73-81.
Kartal, B. (2019). A Theorem on Absolute Summability of Infinite Series. Cumhuriyet Science Journal, 40(3), 563-569. https://doi.org/10.17776/csj.537767