Research Article
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A Study on Generalized Absolute Matrix Summability

Year 2022, Volume: 43 Issue: 2, 316 - 320, 29.06.2022

Ahmet Karakaş

https://doi.org/10.17776/csj.1018894
https://izlik.org/JA55MX66LD

Abstract

In the present paper, generalized absolute matrix summability method of infinite series has been studied. A known theorem on IMI ,summability method has been generalized using the summability method of infinite series. So a new theorem has been established and proved. Some results related to the new theorem also have been obtained.

Keywords

Summability factors Absolute matrix summability Infinite series Hölder inequality Minkowski inequality.

References

  • [1] Cesàro E., Sur la Multiplication des Séries, Bull. Sci. Math., 14 (1890) 114-120 (in French).
  • [2] Abel N.H., Untersuchungen über die Reihe: , J. Reine Angew. Math., 1 (1826) 311-339 (in German).
  • [3] Nörlund N.E., Sur une Application des Fonctions Permutables, Lunds Univ. Arssk., 16 (1919) 1-10 (in French).
  • [4] Riesz M., Sur L’equivalence de Certaines Méthodes de Sommation, Proc. London Math. Soc., 22 (1924) 412-419 (in French).
  • [5] Petersen G.M., Regular matrix transformations. New York: McGraw-Hill, (1966).
  • [6] Das G., Tauberian Theorems for Absolute Nörlund Summability, Proc. London Math. Soc., 19 (1969) 357-384.
  • [7] Kishore N., Hotta G.C., On Summability Factors, Acta Sci. Math. (Szeged), 31 (1970) 9-12.
  • [8] Tanović-Miller N., On Strong Summability, Glas. Mat. Ser. III, 14 (1979) 87-97.
  • [9] Bor H., On Two Summability Methods, Math. Proc. Cambridge Philos. Soc., 97 (1985) 147-149.
  • [10] Bor H., On Local property of Summability of Factored Fourier Series, J. Math. Anal. Appl., 179 (1993) 646-649.
  • [11] Özarslan H.S., Öğdük H.N., Generalizations of Two Theorems on Absolute Summability Methods, Aust. J. Math. Anal. Appl., 1 (2004) Art.no.13.
  • [12] Özarslan H.S., Karakaş A., A New Study on Absolute Summability Factors of Infinite Series, Maejo Int. J. Sci. Technol., 13 (2019) 257-265.
  • [13] Hardy G.H., Divergent series. Oxford: Oxford University Press, (1949).
  • [14] Sulaiman W.T., Inclusion Theorems for Absolute Matrix Summability Methods of an Infinite Series. IV, Indian J. Pure Appl. Math., 34 (2003) 1547-1557.
  • [15] Sulaiman W.T., Some New Factor Theorem for Absolute Summability, Demonstratio Math., 46 (2013) 149-156.
  • [16] Özarslan H.S., Öğdük H.N., On Absolute Matrix Summability Methods, Math. Commun., 12 (2007) 213-220.
  • [17] Özarslan H.S., A Note on Summability Factors, Antarct. J. Math., 7 (2010) 23-30.
  • [18] Özarslan H.S., A New Application of Almost Increasing Sequences, Miskolc Math. Notes, 14 (2013) 201-208.
  • [19] Özarslan H.S., On Generalized Absolute Matrix Summability, Asia Pacific J. Math., 1 (2014) 150-156.
  • [20]Özarslan H.S., Şakar M.Ö., A New Application of Absolute Matrix Summability, Math. Sci. Appl. E-Notes, 3 (2015) 36-43.
  • [21] Özarslan H.S., A New Application of Absolute Matrix Summability, C. R. Acad. Bulgare Sci., 68 (2015) 967-972.
  • [22] Özarslan H.S., A New Study on Generalized Absolute Matrix Summability, Commun. Math. Appl., 7 (2016) 303-309.
  • [23]Özarslan H.S., A New Application of Generalized Almost Increasing Sequences, Bull. Math. Anal. Appl., 8 (2016) 9-15.
  • [24]Özarslan H.S., An Application of δ-quasi Monotone Sequence, Int. J. Anal. Appl., 14 (2017) 134-139.
  • [25]Karakaş A., On Absolute Matrix Summability Factors of Infinite Series, J. Class. Anal., 13 (2018) 133-139.
  • [26]Özarslan H.S., Karakaş A., On Generalized Absolute Matrix Summability of Infinite Series, Commun. Math. Appl., 10 (2019) 439-446.
  • [27] Özarslan H.S., An Application of Absolute Matrix Summability using Almost Increasing and δ-quasi-monotone Sequences, Kyungpook Math. J., 59 (2019) 233-240.
  • [28]Kartal B., On an Extension of Absolute Summability, Konuralp J. Math., 7 (2019) 433-437.
  • [29]Özarslan H.S., A New Factor Theorem for Absolute Matrix Summability, Quaest. Math., 42 (2019) 803-809.

Year 2022, Volume: 43 Issue: 2, 316 - 320, 29.06.2022

Ahmet Karakaş

https://doi.org/10.17776/csj.1018894
https://izlik.org/JA55MX66LD

Abstract

References

  • [1] Cesàro E., Sur la Multiplication des Séries, Bull. Sci. Math., 14 (1890) 114-120 (in French).
  • [2] Abel N.H., Untersuchungen über die Reihe: , J. Reine Angew. Math., 1 (1826) 311-339 (in German).
  • [3] Nörlund N.E., Sur une Application des Fonctions Permutables, Lunds Univ. Arssk., 16 (1919) 1-10 (in French).
  • [4] Riesz M., Sur L’equivalence de Certaines Méthodes de Sommation, Proc. London Math. Soc., 22 (1924) 412-419 (in French).
  • [5] Petersen G.M., Regular matrix transformations. New York: McGraw-Hill, (1966).
  • [6] Das G., Tauberian Theorems for Absolute Nörlund Summability, Proc. London Math. Soc., 19 (1969) 357-384.
  • [7] Kishore N., Hotta G.C., On Summability Factors, Acta Sci. Math. (Szeged), 31 (1970) 9-12.
  • [8] Tanović-Miller N., On Strong Summability, Glas. Mat. Ser. III, 14 (1979) 87-97.
  • [9] Bor H., On Two Summability Methods, Math. Proc. Cambridge Philos. Soc., 97 (1985) 147-149.
  • [10] Bor H., On Local property of Summability of Factored Fourier Series, J. Math. Anal. Appl., 179 (1993) 646-649.
  • [11] Özarslan H.S., Öğdük H.N., Generalizations of Two Theorems on Absolute Summability Methods, Aust. J. Math. Anal. Appl., 1 (2004) Art.no.13.
  • [12] Özarslan H.S., Karakaş A., A New Study on Absolute Summability Factors of Infinite Series, Maejo Int. J. Sci. Technol., 13 (2019) 257-265.
  • [13] Hardy G.H., Divergent series. Oxford: Oxford University Press, (1949).
  • [14] Sulaiman W.T., Inclusion Theorems for Absolute Matrix Summability Methods of an Infinite Series. IV, Indian J. Pure Appl. Math., 34 (2003) 1547-1557.
  • [15] Sulaiman W.T., Some New Factor Theorem for Absolute Summability, Demonstratio Math., 46 (2013) 149-156.
  • [16] Özarslan H.S., Öğdük H.N., On Absolute Matrix Summability Methods, Math. Commun., 12 (2007) 213-220.
  • [17] Özarslan H.S., A Note on Summability Factors, Antarct. J. Math., 7 (2010) 23-30.
  • [18] Özarslan H.S., A New Application of Almost Increasing Sequences, Miskolc Math. Notes, 14 (2013) 201-208.
  • [19] Özarslan H.S., On Generalized Absolute Matrix Summability, Asia Pacific J. Math., 1 (2014) 150-156.
  • [20]Özarslan H.S., Şakar M.Ö., A New Application of Absolute Matrix Summability, Math. Sci. Appl. E-Notes, 3 (2015) 36-43.
  • [21] Özarslan H.S., A New Application of Absolute Matrix Summability, C. R. Acad. Bulgare Sci., 68 (2015) 967-972.
  • [22] Özarslan H.S., A New Study on Generalized Absolute Matrix Summability, Commun. Math. Appl., 7 (2016) 303-309.
  • [23]Özarslan H.S., A New Application of Generalized Almost Increasing Sequences, Bull. Math. Anal. Appl., 8 (2016) 9-15.
  • [24]Özarslan H.S., An Application of δ-quasi Monotone Sequence, Int. J. Anal. Appl., 14 (2017) 134-139.
  • [25]Karakaş A., On Absolute Matrix Summability Factors of Infinite Series, J. Class. Anal., 13 (2018) 133-139.
  • [26]Özarslan H.S., Karakaş A., On Generalized Absolute Matrix Summability of Infinite Series, Commun. Math. Appl., 10 (2019) 439-446.
  • [27] Özarslan H.S., An Application of Absolute Matrix Summability using Almost Increasing and δ-quasi-monotone Sequences, Kyungpook Math. J., 59 (2019) 233-240.
  • [28]Kartal B., On an Extension of Absolute Summability, Konuralp J. Math., 7 (2019) 433-437.
  • [29]Özarslan H.S., A New Factor Theorem for Absolute Matrix Summability, Quaest. Math., 42 (2019) 803-809.
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Ahmet Karakaş 0000-0001-7043-1445

Submission Date November 4, 2021
Acceptance Date May 17, 2022
Publication Date June 29, 2022
DOI https://doi.org/10.17776/csj.1018894
IZ https://izlik.org/JA55MX66LD
Published in Issue Year 2022 Volume: 43 Issue: 2

Cite

APA Karakaş, A. (2022). A Study on Generalized Absolute Matrix Summability. Cumhuriyet Science Journal, 43(2), 316-320. https://doi.org/10.17776/csj.1018894

Cited By

A Note on Summability of Infinite Series
Earthline Journal of Mathematical Sciences
https://doi.org/10.34198/ejms.14424.589594

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