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On the Generalized Absolute Cesàro Summability Methods

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Abstract

In this paper, a theorem on \({\mid{C},\alpha\mid}_k\) summability of an infinite series is generalized for the \(\varphi-{\mid{C},\alpha; \delta\mid}_k\) summability method. Also, a known result dealing with \({\mid{C},1\mid}_k\) summability is given.

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REFERENCES

  1. Bari N.K., Stečkin S.B. "Best approximations and differential properties of two conjugate functions", Trudy Moskov. Math. Obšč. 5, 483-522 (1956) [in Russian].

    MathSciNet  Google Scholar 

  2. Cesàro E. "Sur la multiplication des séries", Bull. Sci. Math. 14, 114-120 (1890).

    MATH  Google Scholar 

  3. Seyhan H. "On the generalized Cesàro summability factors", Acta Comment. Univ. Tartu. Math. 3, 3-6 (1999).

    MathSciNet  MATH  Google Scholar 

  4. Flett T.M. "On an extension of absolute summability and some theorems of Littlewood and Paley", Proc. London Math. Soc. 7 (3), 113-141 (1957).

    Article  MathSciNet  Google Scholar 

  5. Bor H. "On the absolute Cesàro summability factors", Anal. Numér. Théor. Approx. 20 (1–2), 11-14 (1991).

    MathSciNet  MATH  Google Scholar 

  6. Bor H. "Quasimonotone and almost increasing sequences and their new applications", Abstr. Appl. Anal. 2012, 1-6 (2012).

    MathSciNet  MATH  Google Scholar 

  7. Bor H., Özarslan H.S. "A note on absolute summability factors", Adv. Stud. Contemp. Math. 6 (1), 1-11 (2003).

    MathSciNet  MATH  Google Scholar 

  8. Bor H., Seyhan H. "A note on almost increasing sequences", Comment. Math. Prace Mat. 39, 37-42 (1999).

    MathSciNet  MATH  Google Scholar 

  9. Bor H., Srivastava H.M. "Almost increasing sequences and their applications", Int. J. Pure Appl. Math. 3 (1), 29-35 (2002).

    MathSciNet  MATH  Google Scholar 

  10. Özarslan H.S. "On the generalized Cesàro summability factors", Acta Math. Acad. Paedagog. Nyházi 17 (1), 3-7 (2001).

    MathSciNet  MATH  Google Scholar 

  11. Özarslan H.S. "Factors for the \(\varphi-\left|C,\alpha \right|_{k}\) summability", Adv. Stud. Contemp. Math. 5 (1), 25-31 (2002).

    MathSciNet  Google Scholar 

  12. Özarslan H.S. "A note on absolute summability factors", Proc. Indian Acad. Sci. Math. Sci. 113 (2), 165-169 (2003).

    Article  MathSciNet  Google Scholar 

  13. Özarslan H.S. "Absolute Cesàro summability factors", J. Concr. Appl. Math. 5 (3), 231-236 (2007).

    MathSciNet  MATH  Google Scholar 

  14. Özarslan H.S. "On absolute Cesàro summability factors of infinite series", Commun. Math. Anal. 3 (1), 53-56 (2007).

    MathSciNet  MATH  Google Scholar 

  15. Özarslan H.S. "A note on generalized absolute Cesàro summability", J. Comp. Anal. Appl. 12 (3), 581-585 (2010).

    MATH  Google Scholar 

  16. Özarslan H.S. "A note on generalized absolute Cesàro summability", Adv. Pure Appl. Math. 5 (1), 1-3 (2014).

    Article  MathSciNet  Google Scholar 

  17. Seyhan H. "A note on summability methods", Math. Slovaca 49 (2), 201-208 (1999).

    MathSciNet  MATH  Google Scholar 

  18. Sonker S., Munjal A. "Absolute \(\varphi-{\mid{C,\alpha, \beta; \delta}\mid}_k\) summability of infinite series", J. Inequal. Appl. 168, article 168 (2017) (2017).

    MathSciNet  MATH  Google Scholar 

  19. Bor H. "Almost increasing sequences and their new applications", J. Ineq. Appl. 207, article 207 (2013).

    Article  MathSciNet  Google Scholar 

  20. Pati T. "The summability factors of infinite series", Duke Math. J. 21, 271-283 (1954).

    Article  MathSciNet  Google Scholar 

  21. Bosanquet L.S. "A mean value theorem", J. London Math. Soc. 16, 146-148 (1941).

    Article  MathSciNet  Google Scholar 

  22. Mazhar S.M. "Absolute summability factors of infinite series", Kyungpook Math. J. 39 (1), 67-73 (1999).

    MathSciNet  MATH  Google Scholar 

  23. Sulaiman W.T. "On a new application of almost increasing sequences", Bull. Math. Anal. Appl. 4 (3), 29-33 (2012).

    MathSciNet  MATH  Google Scholar 

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Correspondence to H. S. Özarslan.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 11, pp. 34–39.

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Özarslan, H.S. On the Generalized Absolute Cesàro Summability Methods. Russ Math. 65, 29–33 (2021). https://doi.org/10.3103/S1066369X21110049

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  • DOI: https://doi.org/10.3103/S1066369X21110049

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