Research Article
BibTex RIS Cite

A Theorem on Absolute Summability of Infinite Series

Year 2019, Volume: 40 Issue: 3, 563 - 569, 30.09.2019

Bağdagül Kartal

https://doi.org/10.17776/csj.537767
Cited By: 2

Abstract

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.

Keywords

Riesz mean absolute summability almost increasing sequence Hölder inequality Minkowski inequality

References

  • [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.
  • [15] Kartal B., On Generalized Absolute Riesz Summability Method, Commun. Math. Appl., 8-3 (2017) 359-364.
  • [16] Özarslan H.S., A Note on Summability Factors, Indian J. Pure Appl. Math., 33-3 (2002) 361-366.
  • [17] Özarslan H.S., A Note on Quasi Power Increasing Sequences, Indian J. Pure Appl. Math., 34-5 (2003) 727–732.
  • [18] Özarslan H.S., On Summability Factors, Kyungpook Math. J., 43-1 (2003) 107-112.
  • [19] Seyhan H. and Sönmez A., On Summability Factors, Portugal. Math., 54-4 (1997) 393-398.
  • [20] Seyhan H., A Note on Absolute Summability Factors, Far East J. Math. Sci., 6-1 (1998) 157-162.
  • [21] Seyhan H., On the Absolute Summability Factors of Type (A,B), Tamkang J. Math., 30-1 (1999) 59-62.
  • [22] Mazhar S.M., A Note on Absolute Summability Factors, Bull. Inst. Math. Acad. Sinica, 25-3 (1997) 233-242.
  • [23] Özarslan H.S., On Almost Increasing Sequences and Its Applications, Int. J. Math. Math. Sci. 25-5 (2001) 293-298.
  • [24] Mishra K.N. and Srivastava R.S.L., On Absolute Cesàro Summability Factors of Infinite Series, Portugal. Math., 42-1 (1983-84) 53-61.

Sonsuz Serilerin Mutlak Toplanabilmesi Üzerine Bir Teorem

Year 2019, Volume: 40 Issue: 3, 563 - 569, 30.09.2019

Bağdagül Kartal

https://doi.org/10.17776/csj.537767
Cited By: 2

Abstract

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.

Keywords

Riesz ortalaması mutlak toplanabilme

References

  • [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.
  • [15] Kartal B., On Generalized Absolute Riesz Summability Method, Commun. Math. Appl., 8-3 (2017) 359-364.
  • [16] Özarslan H.S., A Note on Summability Factors, Indian J. Pure Appl. Math., 33-3 (2002) 361-366.
  • [17] Özarslan H.S., A Note on Quasi Power Increasing Sequences, Indian J. Pure Appl. Math., 34-5 (2003) 727–732.
  • [18] Özarslan H.S., On Summability Factors, Kyungpook Math. J., 43-1 (2003) 107-112.
  • [19] Seyhan H. and Sönmez A., On Summability Factors, Portugal. Math., 54-4 (1997) 393-398.
  • [20] Seyhan H., A Note on Absolute Summability Factors, Far East J. Math. Sci., 6-1 (1998) 157-162.
  • [21] Seyhan H., On the Absolute Summability Factors of Type (A,B), Tamkang J. Math., 30-1 (1999) 59-62.
  • [22] Mazhar S.M., A Note on Absolute Summability Factors, Bull. Inst. Math. Acad. Sinica, 25-3 (1997) 233-242.
  • [23] Özarslan H.S., On Almost Increasing Sequences and Its Applications, Int. J. Math. Math. Sci. 25-5 (2001) 293-298.
  • [24] Mishra K.N. and Srivastava R.S.L., On Absolute Cesàro Summability Factors of Infinite Series, Portugal. Math., 42-1 (1983-84) 53-61.
There are 24 citations in total.

Details

Primary Language English
Journal Section Natural Sciences
Authors

Bağdagül Kartal 0000-0001-6223-0838

Publication Date September 30, 2019
Submission Date March 9, 2019
Acceptance Date July 8, 2019
Published in Issue Year 2019Volume: 40 Issue: 3

Cite

APA 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

Cited By

Ces\`aro Summability Involving $\delta$-Quasi-Monotone and Almost Increasing Sequences
Journal of New Theory
https://doi.org/10.53570/jnt.1185603
On Necessary and Sufficient Conditions for Absolute Matrix Summability
Earthline Journal of Mathematical Sciences
https://doi.org/10.34198/ejms.12123.112