Arithmetic statistically convergent on neutrosophic normed spaces

Yıl 2023, Cilt: 13 Sayı: 2, 270 - 280, 15.04.2023

Nazmiye Gönül Bilgin

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

Öz

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.

Anahtar Kelimeler

Arithmetic statistically convergence, Ideals, Neutrophic normed spaces.

Nötrosofik normlu uzaylarda aritmetik istatistiksel yakınsaklık

Öz

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.

Anahtar Kelimeler

Aritmetik istatistiksel yakınsaklık, İdealler, Nötrosofik normlu uzaylar.

Kaynakça

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