Rough I_((λ,μ) )-Statistical Convergence of Double Sequences in Gradual Normed Linear Spaces

Year 2022, Volume: 17 Issue: 2, 405 - 428, 25.11.2022

Ömer Kişi , Chiranjib Choudhury

https://doi.org/10.29233/sdufeffd.1158636

Abstract

The aim of this paper is to we examine the notion of gradually rough I_((λ,μ) )-statistical convergence of double sequences in gradual normed linear spaces (GNLS). In addition, we define the concept of gradually rough I_((λ,μ) )-statistical limit set of double sequences and obtain some algebraic and topological features of this set. Theorems are proved in the light of GNLS theory approach. Results are obtained via different perspective and new examples are established to justify the counterparts and indicate existence of introduced notions. We produce significant results that present several fundamental properties of this notion. The results established in this research work supplies an exhaustive foundation in GNLS and make a significant contribution in the theoretical development of GNLS in literature. The original aspect of this study is the first wholly up-to-date and thorough examination of the features and implementations of new introduced notions in GNLS.

Keywords

Gradual normed linear spaces, Rough convergence, I-convergence

Gradual Normlu Uzaylarda Çift Dizilerin Kaba I_((λ,μ) )-İstatistiksel Yakınsaklığı

Abstract

Bu makalenin amacı, gradual normlu lineer uzaylarda (GNLU) çift dizilerin kaba I_((λ,μ) )-istatistiksel yakınsaklığı kavramını incelemektir. Ayrıca, çift dizilerinin gradual kaba I_((λ,μ) )-istatistiksel limit kümesi kavramını tanımlayacak, bu kümenin bazı cebirsel ve topolojik özelliklerini elde edeceğiz. Teoremler, GNLU teorisi yaklaşımı ışığında ispatlanacaktır. Farklı bakış açılarıyla sonuçlar elde edilecek ve karşıtları haklı çıkarmak ve tanıtılan kavramların varlığını göstermek için yeni örnekler üretilecektir. Bu kavramların bazı temel özelliklerini sunan önemli sonuçlar elde edilecektir. Bu araştırma çalışmasında elde edilen sonuçlar, GNLU'da kapsamlı bir temel sağlayacak ve literatürde GNLS'nin teorik gelişimine önemli bir katkı sağlayacaktır. Bu çalışmanın özgün yönü, GNLS'de tanımlanan yeni kavramların özelliklerinin ve uygulamalarının tamamen güncel ve kapsamlı ilk incelemesidir.

Keywords

Gradual normed linear uzaylar, Kaba yakınsaklık, I-yakınsaklık

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