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ON A NEW APPLICATION OF QUASI POWER INCREASING SEQUENCES

  • Received : 2020.06.25
  • Accepted : 2021.04.26
  • Published : 2021.05.30

Abstract

In the present paper, a theorem on 𝜑 - | C, 𝛼; 𝛿 |k summability of an infinite series is obtained by using a quasi 𝛽-power increasing sequence.

Keywords

References

  1. N.K. Bari and S.B. Steckin, Best approximations and differential proprerties of two conjugate functions, Trudy Moskov. Mat. Obsc. 5 (1956), 483-522.
  2. H. Bor, On the absolute Cesaro summability factors, Anal. Numer. Theor. Approx. 20 (1991), 11-14.
  3. H. Bor, An application of quasi power increasing sequences, Aust. J. Math. Anal. Appl. 1 (2004), 1-5.
  4. H. Bor and H.S. Ozarslan, A note on absolute summability factors, Adv. Stud. Contemp. Math. 6 (2003), 1-11.
  5. H. Bor and H.S. Ozarslan, A study on quasi power increasing sequences, Rocky Mountain J. Math. 38 (2008), 801-807. https://doi.org/10.1216/RMJ-2008-38-3-801
  6. H. Bor and H. Seyhan, A note on almost increasing sequences, Comment. Math. Prace Mat. 39 (1999), 37-42.
  7. H. Bor and H.M. Srivastava, Almost increasing sequences and their applications, Int. J. Pure Appl. Math. 3 (2002), 29-35.
  8. L.S. Bosanquet, A mean value theorem, J. London Math. Soc. 16 (1941), 146-148. https://doi.org/10.1112/jlms/s1-16.3.146
  9. E. Cesaro, Sur la multiplication des series, Bull. Sci. Math. 14 (1890), 114-120.
  10. T.M. Flett, On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. London Math. Soc. 7 (1957), 113-141. https://doi.org/10.1112/plms/s3-7.1.113
  11. T.M. Flett, Some more theorems concerning the absolute summability of Fourier series and power series, Proc. London Math. Soc. 8 (1958), 357-387. https://doi.org/10.1112/plms/s3-8.3.357
  12. E. Kogbentliantz, Sur les series absolument sommables par la methode des moyennes arithmetiques, Bull. Sci. Math. 49 (1925), 234-256.
  13. L. Leindler, A new application of quasi power increasing sequences, Publ. Math. Debrecen 58 (2001), 791-796.
  14. H.S. Ozarslan, On the generalized Cesaro summability factors, Acta Math. Acad. Paedagog. Nyhazi. 17 (2001), 3-7.
  15. H.S. Ozarslan, Factors for the φ - |C, α|k summability, Adv. Stud. Contemp. Math. 5 (2002), 25-31.
  16. H.S. Ozarslan, A note on absolute summability factors, Proc. Indian Acad. Sci. Math. Sci. 113 (2003), 165-169. https://doi.org/10.1007/BF02829765
  17. H.S. Ozarslan, Absolute Cesaro summability factors, J. Concr. Appl. Math. 5 (2007), 231-236.
  18. H.S. Ozarslan, On absolute Cesaro summability factors of infinite series, Commun. Math. Anal. 3 (2007), 53-56.
  19. H.S. Ozarslan, A note on generalized absolute Cesaro summability, J. Comp. Anal. Appl. 12 (2010), 581-585.
  20. H.S. Ozarslan, A note on generalized absolute Cesaro summability, Adv. Pure Appl. Math. 5 (2014), 1-3. https://doi.org/10.1515/apam-2013-0037
  21. T. Pati, The summability factors of infinite series, Duke Math. J. 21 (1954), 271-283. https://doi.org/10.1215/S0012-7094-54-02127-4
  22. H. Seyhan, A note on summability methods, Math. Slovaca 49 (1999), 201-208.
  23. H. Seyhan, On the generalized Cesaro summability factors, Acta Comment. Univ. Tartu. Math. 3 (1999), 3-6.