Geometrik hesap tarzına göre Lebesgue dizi uzaylarının bazı geometrik özellikleri

Year 2022, , 395 - 403, 15.04.2022

Birsen Sağır Duyar , İrem Eyüpoğlu

https://doi.org/10.17714/gumusfenbil.1018374

Abstract

Bu çalışmada, geometrik hesap tarzına göre Lebesgue dizi uzayı tanımlandı. İhtiyaç duyulan bazı eşitsizlikler geometrik hesap tarzına göre elde edildi. Bu eşitsizlikler yardımıyla geometrik hesap tarzına göre Lebesgue dizi uzayının konvekslik, kesin konvekslik gibi bazı geometrik özellikleri incelendi.

Keywords

Geometrik hesap tarzı, Kesin konvekslik, Konvekslik, Lebesgue dizi uzayları, Newtonyen olmayan hesap tarzı.

Supporting Institution

Ondokuz Mayıs Üniversitesi

Project Number

PYO.FEN.1904.17.014

Some geometric properties of Lebesgue sequence spaces according to geometric calculation style

Abstract

In this study the Lebesgue sequence space was defined according to geometric calculation style with the help of these inequalities, some geometric properties such as convexity and striclty convexity of Lebesgue sequence space were examined according to the geometric calculation style.

Keywords

Geometric calculation style, Striclty convexity, Convexity, Lebesgue sequence spaces, Non-Newtonian calculation style

Project Number

PYO.FEN.1904.17.014

References

• Bashirov, A.E., & Rıza, M. (2011). On complex multiplicative differentiation. TWMS Journal of Applied and Engineering Mathematics, 1(1), 75- 85.
• Binbaşıoğlu, D., Demiriz, S. & Türkoğlu, D. (2015). Fixed points of non-newtonian contraction mappings on non-newtonian metric spaces. Journal of Fixed Point Theory and Applications, 17(5), 1-12. https://doi.org/10.1007/s11784-015-0271-y.
• Boruah, K. (2017). On some basic properties of geometric real sequences. International Journal of Mathematics Trends and Tecnology. 46(2), 111-117. https://doi.org/10.14445/22315373/IJMTT-V46P519.
• Çakmak, A.F., & Başar, F. (2012). Some new results on sequence spaces with respect to non-newtonian calculus. Journal of Inequalities and Applications. 228, 1-12. https://doi.org/10.1186/1029-242X-2012-228.
• Duyar, C., Sağır, B. & Oğur, O. (2015). Some basic topological properties on non-newtonian real line. British Journal of Mathematics and Computer Science. 9(4), 295-302. https://doi.org/10.9734/BJMCS/2015/17941.
• Duyar, C., & Sağır, B. (2017). Non-Newtonian comment of Lebesgue measure in real numbers. Journal of Mathematics, Article ID 6507013, 1-4. https://doi.org/10.1155/2017/6507013.
• Duyar, C., & Oğur, O. (2017). A note on topology of non-Newtonian real numbers. Journal of Mathematics, 13(6), 11-14.
• Grossmann, M., Katz, R. (1972) . Non-newtonian calculus. (First edition). Massachussests: Lee Press.
• Güngör, N. (2020). Some geometric properties of the non-Newtonian sequence spaces l_p (N) . Mathematica Slovaca. 70(3) ,689-696. https://doi.org/10.1515/ms-2017-0382.
• Gurefe, Y., Kadak, U., Mısırlı, E., & Kurdi, A. (2016). A new look at the classical sequence spaces by using multiplicative calculus. U.P.B. Bull. Series A. 78(2), 9-20.
• Nesin, A. (2012). Analiz 2. Türkiye: Nesin Yayıncılık.
• Oğur, O. (2018). Some geometric properties of weighted Lebesgue spaces L_w^p (G).Facta Universitatis (NISˇ) Series Mathematics and Informatics, 33( 4), 523–530.
• Oğur, O., & Demir, S. (2019). On non-Newtonian measure for α - closed sets. New Trends in Mathematical Sciences, 7(2), 202-207. https://doi.org/10.20852/ntmsci.2019.358.
• 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.
• Türkmen, C., & Başar, F. (2012). Some basic results on the sets of sequences with geometric calculus. Commun Faculty Scientific University Ankara Series. 61(2), 17-34. https://doi.org/10.1501/commual-000000677.
• Yeh, J. (2006). Reel analysis : Theory of measure and integration (Second edition). Singapore: World Scientific Publishing.