On Generalized Absolute Matrix Summability of Infinite Series
DOI:
https://doi.org/10.26713/cma.v10i3.603Keywords:
Summability factors, Absolute matrix summability, Almost increasing sequence, Infinite series, Hölder inequality, Minkowski inequalityAbstract
In this paper, we have generalized a known theorem on \(|\bar{N},p_n|_{k}\) summability factors of infinite series with a new summability method by using almost increasing sequences. This new theorem also includes several new and known results.Downloads
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N. K. Bari and S. B. Steˇckin, Best approximations and differential properties of two conjugate functions, (Russian) Trudy Moskov. Mat. ObšË‡c. 5 (1956), 483 – 522, URL: http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mmo&paperid=56&option_lang=eng.
H. Bor, A note on (|bar{N},p_{n}|_{k}) summability factors of infinite series, Indian J. Pure Appl. Math. 18 (1987), 330 – 336, URL: https://insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a53_330.pdf.
H. Bor, A note on absolute Riesz summability factors, Math. Inequal. Appl. 10 (2007), 619 – 625, DOI: 10.7153/mia-10-58.
H. Bor, Absolute summability factors for infinite series, Indian J. Pure Appl. Math. 19 (1988), 664 – 671, URL: https://insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a52_664.pdf.
H. Bor, On local property of (|bar{N},p_{n};delta|_{k}) summability of factored Fourier series, J. Math. Anal. Appl. 179 (1993), 646 – 649, DOI: 10.1006/jmaa.1993.1375.
H. Bor, On two summability methods, Math. Proc. Camb. Philos Soc. 97 (1985), 147 – 149, DOI: 10.1017/S030500410006268X.
A. N. Gürkan, Absolute Summability Methods of Infinite Series, Ph.D Thesis, Erciyes University, Kayseri (1998).
G. H. Hardy, Divergent Series, Oxford University Press, Oxford (1949), URL: https://sites.math.washington.edu/~morrow/335_17/Hardy-DivergentSeries%202.pdf.
H. S. í–zarslan, A new application of almost increasing sequences, Miskolc Math. Notes 14 (2013), 201 – 208, DOI: 10.18514/MMN.2013.390.
H. S. í–zarslan and H. N. í–ğdük, Generalizations of two theorems on absolute summability methods, Aust. J. Math. Anal. Appl. 1 (2004), Article 13, 7 pages, URL: https://ajmaa.org/searchroot/files/pdf/v1n2/v1i2p13.pdf.
S. M. Mazhar, A note on absolute summability factors, Bull. Inst. Math. Acad. Sinica 25 (1997), 233 – 242, URL: https://web.math.sinica.edu.tw/bulletin/bulletin_old/d253/25304.pdf.
W. T. Sulaiman, Inclusion theorems for absolute matrix summability methods of an infinite series (IV), Indian J.Pure Appl. Math. 34 (11) (2003), 1547 – 1557, https://insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/2000c4ed_1547.pdf.
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