Factors for Generalized Matrix Summability

In [1], Sulaiman has proved a theorem dealing with |A|_{k} summability of the series \sum a_{n} \lambda_n X_n. In the present paper, generalized absolute matrix summability has been studied. The known theorem on |A|_{k} summability has been generalized to the {\varphi}-|A;\delta|_{k} summability method under some suitable conditions.

Anahtar Kelimeler:

summability factors, absolute matrix summability, infinite series, Hölder's inequality, Minkowski's inequality

Factors for Generalized Matrix Summability

Keywords:

Summability factors,

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Sulaiman, W. T. 2013. Some new factor theorem for absolute summability. Demonstratio Math., 46 (1), 149- 156.
Özarslan, H. S. 2018. A new study on generalised absolute matrix summability methods. Maejo Int. J. Sci. Technol., 12 (3), 199-205
Tanović-Miller, N. 1979. On strong summability. Glasnik Mat. Ser. III, 14 (34), 87-97.
Bor, H. 1993. On absolute summability factors. Proc. Amer. Math. Soc., 118 (1), 71-75.
Bor, H. 1996. On |\bar{N},p_n|_k summability factors. Kuwait J. Sci. Eng., 23 (1), 1-5.
Mazhar, S. M. 1997. A note on absolute summability factors. Bull. Inst. Math. Acad. Sinica, 25 (3), 233–242.
Mazhar, S. M. 1999. Absolute summability factors of infinite series. Kyungpook Math. J., 39 (1), 67-73.
Bor, H. 2000. An application of almost increasing and δ-quasi-monotone sequences. JIPAM. J. Inequal. Pure Appl. Math., 1 (2) Article 18, 6pp.
Bor, H. 2001. On absolute Riesz summability factors. Adv. Stud. Contemp. Math. (Pusan), 3 (2), 23-29.
Bor, H. 2007. A note on absolute Riesz summability factors. Math. Inequal. Appl., 10 (3), 619-625.
Özarslan, H. S., Öğdük, H. N. 2007. On absolute matrix summability methods. Math. Commun., 12 (2), 213-220.
Özarslan, H. S. 2010. A note on |A, p_{n}| _{k} summability factors. Antarct. J. Math., 7, 23-30.
Özarslan, H. S., Keten, A. 2013. On a new application of almost increasing sequence. J. Inequal. Appl., 13, 1-7.
Özarslan, H. S. 2013. A new application of almost increasing sequences. Miskolc Math. Notes, 14 (1), 201–208.
Özarslan, H. S. 2014. A note on generalized absolute Riesz summability. An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 60 (1), 51-56.
Özarslan, H. S. 2015. A new application of absolute matrix summability. C. R. Acad. Bulgare Sci., 68 (8), 967-972.
Özarslan, H. S., Şakar, M. Ö. 2015. A new application of absolute matrix summability. Math. Sci. Appl. E-Notes, 3 (1), 36-43.
Özarslan, H. S. 2016. On generalized absolute matrix summability methods. Int. J. Anal. Appl., 12 (1) , 66-70.
Kartal, B. 2017. On generalized absolute Riesz summability method. Commun. Math. Appl., 8 (3), 359-364.
Özarslan, H. S., Karakaş, A. 2017. A new result on the almost increasing sequences. J. Comp. Anal. Appl., 22 (6), 989-998.
Özarslan, H. S., Kartal, B. 2017. A generalization of a theorem of Bor. J. Inequal. Appl., 179, 1-8.
Karakaş, A. 2018. On absolute matrix summability factors of infinite series. J. Class. Anal., 13 (2), 133–139.
Karakaş, A. 2018. N note on absolute summability method involving almost increasing and δ-quasi-monotone sequences. Int. J. Math. Comput. Sci., 13 (1), 73-81.
Kartal, B. 2019. New results for almost increasing sequences. Ann. Univ. Paedagog. Crac. Stud. Math., 18, 85-91.
Özarslan, H. S. 2019. A new factor theorem for absolute matrix summability. Quaest. Math., 42 (6), 803-809.
Özarslan, H. S. 2019. An application of absolute matrix summability using almost increasing and δ-quasi-monotone sequences. Kyungpook Math. J., 59 (2), 233-240.
Özarslan, H. S., Kartal, B. 2020. Absolute matrix summability via almost increasing sequence. Quaest. Math., 43 (10), 1477–1485.