Some sequence spaces defined in n - normed spaces

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Bu tez çalışması beş bölümden oluşmaktadır. Birinci bölümde, bazı temel tanım ve teoremler verildi. İkinci bölümde, 2-norm ve n-norm kavramları ile ilgili bazı temel tanım ve teoremler verildi. İkinci bölümün bir kısmı, üçüncü bölüm ve dördüncü bölümler bu tezin orijinal kısmını oluşturmaktadır. Üçüncü bölümde 2-normlu uzaylarla ilgili kısımlar bulunurken üçüncü bölümde n-normlu uzaylarla ilgili çalışmalar yer almaktadır. Üçüncü bölümde, iki alt başlık yer almaktadır. Bu bölümün ilk kısmında, yeni bir genelleştirilmiş fark matrisi tanımlanarak 2-normlu uzayda bazı -fark istatistiksel yakınsak dizi uzayları tanıtıldı ve bazı topolojik özellikleri incelendi. Aynı bölümün ikinci kısmında ise, Riesz ortalama ile türetilen bazı yeni dizi uzayları tanıtıldı. Ayrıca, ağırlıklı hemen hemen istatistiksel yakınsaklık ve -istatistiksel yakınsaklık kavramları tanıtılarak bu kavramlar arasındaki ilişki incelendi. Dördüncü bölümün ilk kısmında, Lacunary dizisi ve Riesz ortalaması tanımları birleştirilerek n-normlu uzayda ağırlıklı hemen hemen lacunary istatistiksel yakınsaklık olarak adlandırılan yeni bir kavram tanıtıldı. Bu yeni kavramla hemen hemen lacunary istatistiksel yakınsaklık ve ağırlıklı hemen hemen istatiksel yakınsaklık arasındaki ilişki incelendi. Dördüncü bölümün ikinci kısmında, bir sonsuz matris, Orlicz fonksiyonu ve genelleştirilmiş B-fark matrisi kullanılarak bazı dizi uzayları tanıtıldı. Son kısmında ise reel lineer n-normlu uzayında Orlicz fonksiyonu yardımıyla, lacunary dizisi içeren bazı dizi uzayları tanıtılarak bu dizi uzaylarının bazı topolojik özellikleri incelendi. Son bölümde ise elde edilen temel sonuçlar özetlendi.This thesis contains five chapters. In the first chapter, some basic definitions and theorems are given. In the second chapter, some fundamental definitions and theorems related to the concepts of 2-normed space and n-normed space, are given. A part of the second chapter, the third and fourth chapters are original parts of this study. The third chapter is related to the concept of 2-normed space while the studies related with n-normed space are located in the fourth chapter. The third chapter consists of two parts. In the first part of this chapter, a new generalized difference matrix is defined and some -difference statistically convergent sequence spaces in 2-normed space are introduced. In the second part of it, some new sequence spaces derived by Riesz mean are introduced. Further, new concepts of statistical convergence which will be called weighted almost statistical convergence, -statistical convergence in 2-normed space, are defined and some relations between them are investigated. There are three parts in the fourth chapter. In the first part of it, we obtain a new concept of statistical convergence which will be called weighted almost lacunary statistical convergence in n-normed space by combining both of the definitions of lacunary sequence and Riesz mean. We examine some connections between this notion with the concept of almost lacunary statistical convergence and weighted almost statistical convergence, where the base space is a real n-normed space. In the second part of this chapter, some new sequence spaces associated with multiplier sequence by using an infinite matrix, an Orlicz function and generalized -difference operator on a real n-normed space are introduced. In the last part of it, some sequence spaces, involving lacunary sequence, in a real linear n-normed space are introduced. In the last section of this thesis, the main results, which were obtained, are summarized

Generalized difference sequence spaces associated with a multiplier sequence on a real n-normed space

The purpose of this paper is to introduce new sequence spaces associated with a multiplier sequence by using an infinite matrix, an Orlicz function and a generalized B-difference operator on a real n-normed space. Some topological properties of these spaces are examined. We also define a new concept, which will be called (B-Lambda(mu))(n)-statistical A-convergence, and establish some inclusion connections between the sequence space W(A, B-Lambda(mu), p, parallel to., ... , .parallel to) and the set of all (B-Lambda(mu))(n)-statistically A-convergent sequences

On Some Lacunary Almost Convergent Double Sequence Spaces and Banach Limits

The object of this paper is to introduce some new sequence spaces related with the concept of lacunary strong almost convergence for double sequences and also to characterize these spaces through sublinear functionals that both dominate and generate Banach limits and to establish some inclusion relations

On some spaces of lacunary convergent sequences derived by Nörlund-type mean and weighted lacunary statistical convergence

AbstractIn this paper, we define some new sequence spaces of lacunary convergent sequences derived by Nörlund-type (Riesz) mean, which shall be denoted by |N‾,pr,θ| and (N‾,pr,θ), and investigate some relations between the sequence space |N‾,pr,θ| with the spaces ∣wθ∣ and |N‾,pn|. Further, we define a new concept, named weighted lacunary statistical convergence and examine some connections between this notion with the concept of lacunary statistical convergence and weighted statistical convergence. Also, some topological properties of these new sequence spaces are investigated

Some generalized difference statistically convergent sequence spaces in 2-normed space

In this paper, we define a new generalized difference matrix Bn(m) and introduce some Bn(m)-difference statistically convergent sequence spaces in a real linear 2-normed space. We also investigate some topological properties of these spaces

Weighted Lacunary Statistical Convergence

In this paper, we extend the concept of weighted lacunary statistical convergence to Hausdorff locally convex topological linear spaces and present some inclusion theorems

Variations of some star selection properties

4th International Conference of Mathematical Sciences (ICMS) -- JUN 17-21, 2020 -- Maltepe Univ, ELECTR NETWORKIn this paper we introduce some new types of star covering properties which we call set (strongly) star Menger, set (strongly) star Rothberger, set (strongly) star Hurewicz properties. We consider also weaker versions of these properties, discuss their relationships with some other selective covering properties, and study topological properties of introduced classes of spaces