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On Non-Newtonian Power Series and Its Applications

Year 2020, Volume: 8 Issue: 2, 294 - 303, 27.10.2020

Abstract

The purpose of this study is to examine *-Abel and *-Dirichlet tests, *-power series,

References

  • [1] A.E. Bashirov,E.M. Kurpınar, A. Ozyapıcı, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337, (2008), 36-48.
  • [2] A. Bashirov, M. Rıza, On complex multiplicative differentiation, TWMS J. Appl. Engrg. Math. 1(1) (2011), 75-85.
  • [4] Z. Cakır, Spaces of continuous and bounded function sover the field of geometric complex numbers, J. Inequal. Appl. 2013, 363, 5pages.
  • [5] A.F. Cakmak, F. Basar, On the classical sequence spaces and non-newtonian calculus, J. Inequal. Appl. 2012, Art.ID932734,13pp.
  • [6] C. Duyar, B.Sagir, O. Ogur, Some basic topological properties on non-Newtonian real line, British J. Math. Comput. Sci. 9, no.4, (2015), 300–307.
  • [7] C. Duyar, M. Erdogan, On non-Newtonian real number series, IOSR J. Math. 12, iss.6, ver.IV, (2016), 34–48.
  • [8] C. Duyar, O.Ogur, A note on topology of non-Newtonian real numbers, IOSR J. Math. 13, iss. 6, ver.IV, (2017), 11–14.
  • [9] M. Erdogan, C. Duyar, Non-Newtonian Improper Integrals ,Journal of Science and Arts,1 (42), (2018), 49-74. [10] M. Grossman, R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, Massachusetts,1972.
  • [11] M. Grossman, The First Nonlinear System of Differential and Integral Calculus, MATHCO, Massachusetts, 1979.
  • [12] J. Grossman, Meta-Calculus: Differential and Integral, Archimedes Foundation, Rockport Massachusetts, 1sted., 1981.
  • [13] U. Kadak, Cesaro Summable Sequence Spaces over the Non-Newtonian Complex Field, J. Probab. Stat. 2016, (2016), 1-10.
  • [14] B. Sagır, F. Erdogan, On the function sequences and series in the non-Newtonian calculus, Journal of Science and Arts, 4(49), (2019), 915-936.
  • [15] S. Tekin, F. Basar, Certain sequence spaces over the non-Newtonian complex field, Abstr. Appl. Anal. 2013, Art.ID739319, 11pages.
  • [16] C. Turkmen, F. Basar, Some basic results on the geometric calculus, Commun. Fac. Sci. Univ. Ankara, Ser. A1 Math. Stat. 61 (2) (2012), 17-34.
  • [17] A. Uzer, Multiplicative type complex calculus as analternative to the classical calculus, Comput. Math. Appl. 60, (2010), 2725-2737.
  • [18] E. Unlüyol, S. Salas, Convexity and Hermite-Hadamard type inequality via Non-Newtonian calculus, Konuralp Journal of Mathematics, 7, (2019), 352-358.
Year 2020, Volume: 8 Issue: 2, 294 - 303, 27.10.2020

Abstract

References

  • [1] A.E. Bashirov,E.M. Kurpınar, A. Ozyapıcı, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337, (2008), 36-48.
  • [2] A. Bashirov, M. Rıza, On complex multiplicative differentiation, TWMS J. Appl. Engrg. Math. 1(1) (2011), 75-85.
  • [4] Z. Cakır, Spaces of continuous and bounded function sover the field of geometric complex numbers, J. Inequal. Appl. 2013, 363, 5pages.
  • [5] A.F. Cakmak, F. Basar, On the classical sequence spaces and non-newtonian calculus, J. Inequal. Appl. 2012, Art.ID932734,13pp.
  • [6] C. Duyar, B.Sagir, O. Ogur, Some basic topological properties on non-Newtonian real line, British J. Math. Comput. Sci. 9, no.4, (2015), 300–307.
  • [7] C. Duyar, M. Erdogan, On non-Newtonian real number series, IOSR J. Math. 12, iss.6, ver.IV, (2016), 34–48.
  • [8] C. Duyar, O.Ogur, A note on topology of non-Newtonian real numbers, IOSR J. Math. 13, iss. 6, ver.IV, (2017), 11–14.
  • [9] M. Erdogan, C. Duyar, Non-Newtonian Improper Integrals ,Journal of Science and Arts,1 (42), (2018), 49-74. [10] M. Grossman, R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, Massachusetts,1972.
  • [11] M. Grossman, The First Nonlinear System of Differential and Integral Calculus, MATHCO, Massachusetts, 1979.
  • [12] J. Grossman, Meta-Calculus: Differential and Integral, Archimedes Foundation, Rockport Massachusetts, 1sted., 1981.
  • [13] U. Kadak, Cesaro Summable Sequence Spaces over the Non-Newtonian Complex Field, J. Probab. Stat. 2016, (2016), 1-10.
  • [14] B. Sagır, F. Erdogan, On the function sequences and series in the non-Newtonian calculus, Journal of Science and Arts, 4(49), (2019), 915-936.
  • [15] S. Tekin, F. Basar, Certain sequence spaces over the non-Newtonian complex field, Abstr. Appl. Anal. 2013, Art.ID739319, 11pages.
  • [16] C. Turkmen, F. Basar, Some basic results on the geometric calculus, Commun. Fac. Sci. Univ. Ankara, Ser. A1 Math. Stat. 61 (2) (2012), 17-34.
  • [17] A. Uzer, Multiplicative type complex calculus as analternative to the classical calculus, Comput. Math. Appl. 60, (2010), 2725-2737.
  • [18] E. Unlüyol, S. Salas, Convexity and Hermite-Hadamard type inequality via Non-Newtonian calculus, Konuralp Journal of Mathematics, 7, (2019), 352-358.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Birsen Sağır Duyar

Fatmanur Erdogan

Publication Date October 27, 2020
Submission Date December 22, 2019
Acceptance Date May 22, 2020
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

APA Sağır Duyar, B., & Erdogan, F. (2020). On Non-Newtonian Power Series and Its Applications. Konuralp Journal of Mathematics, 8(2), 294-303.
AMA Sağır Duyar B, Erdogan F. On Non-Newtonian Power Series and Its Applications. Konuralp J. Math. October 2020;8(2):294-303.
Chicago Sağır Duyar, Birsen, and Fatmanur Erdogan. “On Non-Newtonian Power Series and Its Applications”. Konuralp Journal of Mathematics 8, no. 2 (October 2020): 294-303.
EndNote Sağır Duyar B, Erdogan F (October 1, 2020) On Non-Newtonian Power Series and Its Applications. Konuralp Journal of Mathematics 8 2 294–303.
IEEE B. Sağır Duyar and F. Erdogan, “On Non-Newtonian Power Series and Its Applications”, Konuralp J. Math., vol. 8, no. 2, pp. 294–303, 2020.
ISNAD Sağır Duyar, Birsen - Erdogan, Fatmanur. “On Non-Newtonian Power Series and Its Applications”. Konuralp Journal of Mathematics 8/2 (October 2020), 294-303.
JAMA Sağır Duyar B, Erdogan F. On Non-Newtonian Power Series and Its Applications. Konuralp J. Math. 2020;8:294–303.
MLA Sağır Duyar, Birsen and Fatmanur Erdogan. “On Non-Newtonian Power Series and Its Applications”. Konuralp Journal of Mathematics, vol. 8, no. 2, 2020, pp. 294-03.
Vancouver Sağır Duyar B, Erdogan F. On Non-Newtonian Power Series and Its Applications. Konuralp J. Math. 2020;8(2):294-303.
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