Difference sequence spaces derived by using a generalized weighted mean

AbstractIn this work, we define new sequence spaces by combining a generalized weighted mean and a difference operator. Afterward, we investigate topological structures, which have completeness, AK-property, and AD-property. Also, we compute the α-, β- and γ-duals, and obtain bases for these sequence spaces. Finally, the necessary and sufficient conditions on an infinite matrix belonging to the classes (c(u,v,Δ):ℓ∞) and (c(u,v,Δ):c) are obtained

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

The sequence space bv and some applications

In this work, we give well-known results related to some properties, dual spaces and matrix transformations of the sequence space bv and introduce the matrix domain of space bv with arbitrary triangle matrix A. Afterward, we choose the matrix A as Ces\`aro mean of order one, generalized weighted mean and Riesz mean and compute alpha-; beta- gamma-duals of these spaces. And also, we characterize the matrix classes of the new spaces.Comment: 9 page

Some Paranormed Difference Sequence Spaces of Order mm Derived by Generalized Means and Compact Operators

We have introduced a new sequence space $l(r, s, t, p ;\Delta^{(m)})$ combining by using generalized means and difference operator of order $m$. We have shown that the space $l(r, s, t, p ;\Delta^{(m)})$ is complete under some suitable paranorm and it has Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of this space is computed and also obtained necessary and sufficient conditions for some matrix transformations from $l(r, s, t, p; \Delta^{(m)})$ to $l_{\infty}, l_1$. Finally, we obtained some identities or estimates for the operator norms and the Hausdorff measure of noncompactness of some matrix operators on the BK space $l_{p}(r, s, t ;\Delta^{(m)})$ by applying the Hausdorff measure of noncompactness.Comment: Please withdraw this paper as there are some logical gap in some results. 20 pages. arXiv admin note: substantial text overlap with arXiv:1307.5883, arXiv:1307.5817, arXiv:1307.588

The Method of almost convergence with operator of the form fractional order and applications

The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those concepts are presented. Second, we construct the almost convergent spaces with fractional order difference operator and compute dual spaces which are help us in the characterization of matrix mappings. After we characterize to the matrix transformations, we give some examples.Comment: 20 pages, 4 table