BibTex RIS Cite

Mercerian theorem for four dimensional matrices

Year 2016, Volume: 65 Issue: 1, 147 - 156, 01.02.2016
https://doi.org/10.1501/Commua1_0000000750

References

  • A. Pringsheim, Zur theorie der zweifach unend lichen Zahlenfolgen, Math. Ann. 53 (1900), –321.
  • J. Boos, Classical and Modern Methods in Summability, Oxford University Press Inc., New York, 2000.
  • F. Móricz, Extensions of the spaces c and c0from single to double sequences, Acta Math. Hungar. 57 (1991), 129–136.
  • F. Ba¸sar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, ·Istanbul, 2012.
  • M. Mursaleen, S.A. Mohiuddine, Convergence Methods For Double Sequences and Applica- tions, Springer, New Delhi Heidelberg New York Dordrecht London, 2014.
  • G.H. Hardy, On the convergence of certain multiple series, Proc. Camb. Phil. Soc. 19 (1917), –95.
  • M. Unver, Characterization of multidimensional A-strong convergence, Studia Sci. Math. Hungar. 50 (1) (2013), 17–25.
  • F. Móricz, B.E. Rhoades, Almost convergence of double sequences and strong regularity of summability matrices, Proc. Camb. Phil. Soc. 104 (1988), 283–294.
  • R.F. Patterson, Four dimensional characterization of bounded double sequences, Tamkang J. Math. 35 (2004), 129–134.
  • B.C. Tripathy, Statistically convergent double sequences, Tamkang J. Math. 34 (3) (2003), –237.
  • J. Boos, T. Leiger, K. Zeller, Consistency theory for SMmethods, Acta Math. Hungar. 76 (1-2) (1997), 109–142.
  • C.R. Adams, On non-factorable transformations of double sequences, Proc. Natl. Acad. Sci. USA. 19 (5) (1933), 564–567.
  • R.C. Cooke, In…nite Matrices and Sequence Spaces, Macmillan and Co. Limited, London, M. Zeltser, On conservative matrix methods for double sequence spaces, Acta Math. Hung. (3) (2002), 225–242.
  • A. Wilansky, Summability through Functional Analysis, North-Holland Mathematics Studies , Amsterdam New York Oxford, 1984.
  • G.M. Robison, Divergent double sequences and series, Trans. Amer. Math. Soc. 28 (1926), –73.
  • H.J. Hamilton, Transformations of multiple sequences, Duke Math. J. 2 (1936), 29–60.
  • J. Mercer,On the limits of real variants, Proc. London Math. Soc. 2 (1) (1907), no. 5, 206–
  • G.H. Hardy, Divergent Series, Oxford Univ. Press, London, 1949.
  • I.J Maddox, Elements of Functional Analysis, Second edition, Cambridge University Press, Cambridge, 1988.
  • M. Ye¸silkayagil, F. Ba¸sar, Domain of Riesz mean in some spaces of double sequences, under communication. Current address : Department of Mathematics, Fatih University, The Hadımköy Campus, Büyükçekmece, 34500 ·Istanbul, Turkey
  • E-mail address : fbasar@fatih.edu.tr & feyzibasar@gmail.com Current address : Medine Ye¸silkayagil: Department of Mathematics, U¸sak University, 1 Eylül Campus, 64200 U¸sak, Turkey
  • E-mail address : medine.yesilkayagil@usak.edu.tr
Year 2016, Volume: 65 Issue: 1, 147 - 156, 01.02.2016
https://doi.org/10.1501/Commua1_0000000750

References

  • A. Pringsheim, Zur theorie der zweifach unend lichen Zahlenfolgen, Math. Ann. 53 (1900), –321.
  • J. Boos, Classical and Modern Methods in Summability, Oxford University Press Inc., New York, 2000.
  • F. Móricz, Extensions of the spaces c and c0from single to double sequences, Acta Math. Hungar. 57 (1991), 129–136.
  • F. Ba¸sar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, ·Istanbul, 2012.
  • M. Mursaleen, S.A. Mohiuddine, Convergence Methods For Double Sequences and Applica- tions, Springer, New Delhi Heidelberg New York Dordrecht London, 2014.
  • G.H. Hardy, On the convergence of certain multiple series, Proc. Camb. Phil. Soc. 19 (1917), –95.
  • M. Unver, Characterization of multidimensional A-strong convergence, Studia Sci. Math. Hungar. 50 (1) (2013), 17–25.
  • F. Móricz, B.E. Rhoades, Almost convergence of double sequences and strong regularity of summability matrices, Proc. Camb. Phil. Soc. 104 (1988), 283–294.
  • R.F. Patterson, Four dimensional characterization of bounded double sequences, Tamkang J. Math. 35 (2004), 129–134.
  • B.C. Tripathy, Statistically convergent double sequences, Tamkang J. Math. 34 (3) (2003), –237.
  • J. Boos, T. Leiger, K. Zeller, Consistency theory for SMmethods, Acta Math. Hungar. 76 (1-2) (1997), 109–142.
  • C.R. Adams, On non-factorable transformations of double sequences, Proc. Natl. Acad. Sci. USA. 19 (5) (1933), 564–567.
  • R.C. Cooke, In…nite Matrices and Sequence Spaces, Macmillan and Co. Limited, London, M. Zeltser, On conservative matrix methods for double sequence spaces, Acta Math. Hung. (3) (2002), 225–242.
  • A. Wilansky, Summability through Functional Analysis, North-Holland Mathematics Studies , Amsterdam New York Oxford, 1984.
  • G.M. Robison, Divergent double sequences and series, Trans. Amer. Math. Soc. 28 (1926), –73.
  • H.J. Hamilton, Transformations of multiple sequences, Duke Math. J. 2 (1936), 29–60.
  • J. Mercer,On the limits of real variants, Proc. London Math. Soc. 2 (1) (1907), no. 5, 206–
  • G.H. Hardy, Divergent Series, Oxford Univ. Press, London, 1949.
  • I.J Maddox, Elements of Functional Analysis, Second edition, Cambridge University Press, Cambridge, 1988.
  • M. Ye¸silkayagil, F. Ba¸sar, Domain of Riesz mean in some spaces of double sequences, under communication. Current address : Department of Mathematics, Fatih University, The Hadımköy Campus, Büyükçekmece, 34500 ·Istanbul, Turkey
  • E-mail address : fbasar@fatih.edu.tr & feyzibasar@gmail.com Current address : Medine Ye¸silkayagil: Department of Mathematics, U¸sak University, 1 Eylül Campus, 64200 U¸sak, Turkey
  • E-mail address : medine.yesilkayagil@usak.edu.tr
There are 22 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Medine Yeşilkayagil This is me

Fevzi Başar This is me

Publication Date February 1, 2016
Published in Issue Year 2016 Volume: 65 Issue: 1

Cite

APA Yeşilkayagil, M., & Başar, F. (2016). Mercerian theorem for four dimensional matrices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(1), 147-156. https://doi.org/10.1501/Commua1_0000000750
AMA Yeşilkayagil M, Başar F. Mercerian theorem for four dimensional matrices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2016;65(1):147-156. doi:10.1501/Commua1_0000000750
Chicago Yeşilkayagil, Medine, and Fevzi Başar. “Mercerian Theorem for Four Dimensional Matrices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65, no. 1 (February 2016): 147-56. https://doi.org/10.1501/Commua1_0000000750.
EndNote Yeşilkayagil M, Başar F (February 1, 2016) Mercerian theorem for four dimensional matrices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 1 147–156.
IEEE M. Yeşilkayagil and F. Başar, “Mercerian theorem for four dimensional matrices”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 65, no. 1, pp. 147–156, 2016, doi: 10.1501/Commua1_0000000750.
ISNAD Yeşilkayagil, Medine - Başar, Fevzi. “Mercerian Theorem for Four Dimensional Matrices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/1 (February 2016), 147-156. https://doi.org/10.1501/Commua1_0000000750.
JAMA Yeşilkayagil M, Başar F. Mercerian theorem for four dimensional matrices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:147–156.
MLA Yeşilkayagil, Medine and Fevzi Başar. “Mercerian Theorem for Four Dimensional Matrices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 65, no. 1, 2016, pp. 147-56, doi:10.1501/Commua1_0000000750.
Vancouver Yeşilkayagil M, Başar F. Mercerian theorem for four dimensional matrices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(1):147-56.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.