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Newtonyen Olmayan Lebesgue Ölçüsü

Year 2020, , 134 - 139, 15.01.2020
https://doi.org/10.17714/gumusfenbil.598468

Abstract




Bu çalışmada, Newtonyen olmayan sınırlı
kümelerin iç ve dış ölçü  kavramları
verildi .

Ayrıca, Newtonyen olmayan kümelerin Lebesgue anlamında ölçüsü
tanımlanarak ilgili temel teoremler verildi.

References

  • Bashirov, A.E. ve Rıza, M., 2011. On complex multiplicative differentation, TWMS Journal of Applied and Engineering Mathematics, 1(1), 75-85.
  • Çakmak, A. F. ve Başar F., 2012. Some new results on sequence spaces with respect to non-Newtonian calculus, Journal of Inequalities and Applications, 228, 1-12.
  • Duyar, C. ve Oğur, O., 2017. A note on topology of non-Newtonian real numbers, Journal of Mathematics, 13(6), 11-14.
  • Duyar, C., Sağır, B. ve Oğur, O., 2015. Some basic topological properties on non-Newtonian real line, British Journal of Mathematics and Computer Science, 9(4), 300-307.
  • Duyar, C. ve Sağır B., 2017. Non-Newtonian comment of Lebesgue measure in real numbers, Journal of Mathematics, Article ID 6507013, 1-4.
  • Erdoğan, M., 2016. Newtonyen olmayan reel sayı serileri ve has olmayan integraller, Yüksek Lisans Tezi, Ondokuz Mayıs Üniversitesi Fen Bilimleri Enstitüsü, Samsun, 89s.
  • Florak, L. ve Assen, H. V., 2012. Multiplicative calculus in biomedical image anaysis, Journal of Mathematical Imaging and Vision, 42(1), 64-75.
  • Grossman, M. ve Katz, R., 1972. Non-Newtonian calculus, 1 st ed. Press, Piagen Cove Massuchusets.
  • Kadak, U., 2015. Newtonyen olmayan analiz ve çeşitli uygulamaları, Doktora Tezi, Gazi Üniversitesi Fen Bilimleri Enstitüsü, Ankara, 100s.
  • Natanson, I. P., 1964. Theory of function of a real variable, vol 1, Frederick Ungar Publishing Co., New York, NY, USA.
  • Oğur, O. ve Demir, S., 2019. On non-Newtonian measure for closed sets, New Trends in Mathematical Sciences, 7(2), 202-207.

Non-Newtonian Lebesgue Measure

Year 2020, , 134 - 139, 15.01.2020
https://doi.org/10.17714/gumusfenbil.598468

Abstract

In this paper,
definitions of the inner and outer measure of non-Newtonian bounded sets are
given. Also, Lebesgue measure of non-Newtonian sets is defined and related
theorems are given.

References

  • Bashirov, A.E. ve Rıza, M., 2011. On complex multiplicative differentation, TWMS Journal of Applied and Engineering Mathematics, 1(1), 75-85.
  • Çakmak, A. F. ve Başar F., 2012. Some new results on sequence spaces with respect to non-Newtonian calculus, Journal of Inequalities and Applications, 228, 1-12.
  • Duyar, C. ve Oğur, O., 2017. A note on topology of non-Newtonian real numbers, Journal of Mathematics, 13(6), 11-14.
  • Duyar, C., Sağır, B. ve Oğur, O., 2015. Some basic topological properties on non-Newtonian real line, British Journal of Mathematics and Computer Science, 9(4), 300-307.
  • Duyar, C. ve Sağır B., 2017. Non-Newtonian comment of Lebesgue measure in real numbers, Journal of Mathematics, Article ID 6507013, 1-4.
  • Erdoğan, M., 2016. Newtonyen olmayan reel sayı serileri ve has olmayan integraller, Yüksek Lisans Tezi, Ondokuz Mayıs Üniversitesi Fen Bilimleri Enstitüsü, Samsun, 89s.
  • Florak, L. ve Assen, H. V., 2012. Multiplicative calculus in biomedical image anaysis, Journal of Mathematical Imaging and Vision, 42(1), 64-75.
  • Grossman, M. ve Katz, R., 1972. Non-Newtonian calculus, 1 st ed. Press, Piagen Cove Massuchusets.
  • Kadak, U., 2015. Newtonyen olmayan analiz ve çeşitli uygulamaları, Doktora Tezi, Gazi Üniversitesi Fen Bilimleri Enstitüsü, Ankara, 100s.
  • Natanson, I. P., 1964. Theory of function of a real variable, vol 1, Frederick Ungar Publishing Co., New York, NY, USA.
  • Oğur, O. ve Demir, S., 2019. On non-Newtonian measure for closed sets, New Trends in Mathematical Sciences, 7(2), 202-207.
There are 11 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Oğuz Oğur 0000-0002-3206-5330

Sezgin Demir 0000-0003-1036-1363

Publication Date January 15, 2020
Submission Date July 30, 2019
Acceptance Date October 23, 2019
Published in Issue Year 2020

Cite

APA Oğur, O., & Demir, S. (2020). Newtonyen Olmayan Lebesgue Ölçüsü. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 10(1), 134-139. https://doi.org/10.17714/gumusfenbil.598468