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A Study on Generalized Absolute Matrix Summability

Year 2022, , 316 - 320, 29.06.2022
https://doi.org/10.17776/csj.1018894

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.

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, , 316 - 320, 29.06.2022
https://doi.org/10.17776/csj.1018894

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 Natural Sciences
Authors

Ahmet Karakaş 0000-0001-7043-1445

Publication Date June 29, 2022
Submission Date November 4, 2021
Acceptance Date May 17, 2022
Published in Issue Year 2022

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

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