Arithmetic statistically convergent on neutrosophic normed spaces

Year 2023, , 270 - 280, 15.04.2023

Nazmiye Gönül Bilgin

https://doi.org/10.17714/gumusfenbil.1180772

Abstract

This work is concerned with several important different types of convergence that will be described on neutrosophic normed spaces. In the study, arithmetic convergence was combined with different types of statistical convergence and then integrated into the structure of neutrosophic spaces established through the membership function. For this purpose, in the neutrosophic normed space, firstly, the concepts of arithmetic convergence and arithmetic statistical convergence are given, then some important definitions that can be established with lacunary sequences and ideal structures and some relationships between convergent sequences in this sense are examined. Furthermore, new convergence definitions were established by evaluating lambda sequences together with arithmetic convergence and statistical convergence with the help of neutrosophic normed space structure properties. Finally, with the help of the definition of graduated convergence, the inclusion relation between the two set is given.

Keywords

Arithmetic statistically convergence, Ideals, Neutrophic normed spaces.

Nötrosofik normlu uzaylarda aritmetik istatistiksel yakınsaklık

Abstract

Bu çalışma, nötrosofik normlu uzaylar üzerinde tanımlanacak olan önemli birkaç yakınsaklık türü ile ilgilidir. Çalışmada, aritmetik yakınsaklık, farklı istatistiksel yakınsaklık türleri ile birleştirilmiş ve daha sonra üyelik fonksiyonu yardımıyla kurulan nötrosofik uzayların yapısına dahil edilmiştir. Bu amaçla nötrosofik normlu uzayda öncelikle aritmetik yakınsaklık ve aritmetik istatistiksel yakınsaklık kavramları verilmiş, ardından lacunary diziler ve ideal yapılar ile kurulabilecek bazı önemli tanımlar ve yakınsak diziler arasında bu anlamdaki bazı ilişkiler incelenmiştir. Ayrıca nötrosofik normlu uzay yapısı özellikleri yardımıyla lambda diziler; aritmetik yakınsaklık ve istatistiksel yakınsaklıkla birlikte değerlendirilerek yeni yakınsaklık tanımları kurulmuştur. Son olarak dereceli yakınsaklık tanımı yardımıyla iki küme arasında kapsama bağıntısı verilmiştir.

Keywords

Aritmetik istatistiksel yakınsaklık, İdealler, Nötrosofik normlu uzaylar.

References

• Esi, A., & Hazarika, B. (2013). λ-ideal convergence in intuitionistic fuzzy 2-normed linear space. Journal of Intelligent & Fuzzy Systems, 24(4), 725-732.
• Gonul Bilgin, N. (2022a). Rough statistical convergence in neutrosophic normed spaces. Euroasia Journal of Mathematics, Engineering, Natural & Medical Sciences, 9(21), 47-55.
• Gonul Bilgin, N. (2022b). Hibrid Δ-statistical convergence for neutrosophic normed space. Journal of Mathematics, 2022, 1-10. https://doi.org/10.1155/2022/3890308
• Gonul Bilgin, N., Pamučar, D., & Riaz, M. (2022). Fermatean neutrosophic topological spaces and an application of neutrosophic kano method. Symmetry, 14(11), 2442. https://doi.org/10.3390/sym14112442
• Khan, V. A., Khan, M. D., & Ahmad, M. (2021). Some new type of lacunary statistically convergent sequences in neutrosophic normed space. Neutrosophic Sets and Systems, 42(1), 239-252.
• Kirisci, M., & Simsek N. (2020). Neutrosophic normed spaces and statistical convergence. The Journal of Analysis, 1-15. https://doi.org/10.1007/s41478-020-00234-0
• Kisi, O. (2020). Lacunary statistical convergence of sequences in neutrosophic normed spaces. 4th International Conference on Mathematics: an Istanbul Meeting for World Mathematicians (pp. 345–354), Istanbul.
• Kisi, O. (2021a). Ideal convergence of sequences in neutrosophic normed spaces. Journal of Intelligent & Fuzzy Systems, (Preprint), 1-10. https://doi.org/ 10.3233/JIFS-201568
• Kisi, O. (2021b). On I_θ arithmetic convergence. Malaya Journal of Matematik, 9(3), 64-71.
• Kisi, O. (2021c). On I_{θ}-convergence in neutrosophic normed spaces. Fundamental Journal of Mathematics and Applications, 4(2), 67-76. https://doi.org/10.33401/fujma.873029
• Kisi, O. (2022). I-lacunary arithmetic statistical convergence. Journal of Applied Mathematics & Informatics, 40(1-2), 327-339. https://doi.org/10.14317/jami.2022.327.
• Kisi, O., & Gurdal, V. (2022a). Triple lacunary Δ-statistical convergence in neutrosophic normed spaces. Konuralp Journal of Mathematics, 10(1), 127-133.
• Kisi, O., & Gurdal, V. (2022b). On triple difference sequences of real numbers in neutrosophic normed spaces. Communications in Advanced Mathematical Sciences, 5(1), 35-45. https://doi.org/10.33434/cams.1025928
• Kostyrko, P., Šalát, T., & Wilczyński, W. (2000). I-convergence. Real Analysis Exchange, 669-685.
• Mursaleen M. (2000). λ-statistical convergence. Math Slovaca 50(1), 111–115.
• Smarandache F. (1998). Neutrosophy. neutrosophic probability, set and logic (1st ed.). ProQuest Information & Learning.
• Riaz, M., Almalki, Y., Batool, S., & Tanveer, S. (2022a). Topological structure of single-valued neutrosophic hesitant fuzzy sets and data analysis for uncertain supply chains. Symmetry, 14(7), 1382. https://doi.org/10.3390/sym 14071382
• Riaz, M., Ishtiaq, U., Park, C., Ahmad, K., & Uddin, F. (2022b). Some fixed point results for ξ-chainable neutrosophic and generalized neutrosophic cone metric spaces with application. AIMS Mathematics, 7(8), 14756-14784. https://doi.org/10.3934/math.2022811
• Ruckle, W. H. (2012). Arithmetical summability. Journal of Mathematical Analysis and Applications, 396(2), 741-748. https://doi.org/10.1016/j.jmaa.2012.06.048
• Yaying, T., & Hazarika, B. (2018). On lacunary arithmetic convergence. Proceedings of the Jangjeon Mathematical Society. 21(3), 507-513.
• Yaying, T., & Hazarika, B. (2020). Lacunary arithmetic statistical convergence. National Academy Science Letters, 43(6), 547-551. https://doi.org/10.1007/s40009-020-00910-6