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Öğe 4d First order q-Euler matrix operator and its domain in the space Ls(Springer Basel Ag, 2023) Demiriz, Serkan; Erdem, SezerIn the present study, firstly, it is described the 4 dimensional (4d) first order q-Euler matrix by the aid of q-analogue. After that, it is obtained a new double sequence space as the domain of this aforementioned matrix in L-s space and examined some properties of this space.Öğe Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space(Emrah Evren KARA, 2024) Demiriz, Serkan; Erdem, SezerIn this study, it is introduced the regular Mersenne matrix operator which is obtained by using Mersenne numbers and examined sequence spaces described as the domain of this matrix in the space of $p$-summable sequences for $1\leq p \leq \infty$. After that, it investigated some properties and inclusion relations, established the Schauder basis, and stated $\alpha-$, $\beta-$, and $\gamma-$duals of the aforementioned spaces. Additionally, it is characterized by the matrix classes from newly described spaces to classical sequence spaces. Finally, we studied the compactness of matrix operators on related sequence spaces.Öğe Motzkin Sequence Spaces and Motzkin Core(Taylor & Francis Inc, 2024) Erdem, Sezer; Demiriz, Serkan; Sahin, AdemIn the current work, it is constructed the Motzkin matrix obtained by using Motzkin numbers M=(mrs) and is examined the sequence spaces c(M) and c0(M) described as the domain of Motzkin matrix M in the spaces c and c0, respectively. It is investigated topological properties, established Schauder basis and stated Kothe duals of the aforementioned spaces. Additionally, it is characterized the matrix classes from c(M) and c0(M) to the classical sequence spaces and vice versa. Finally, Motzkin core of any sequence is presented and it is elaborated some inclusion relation of just described new type of core.Öğe ON THE CONVERGENT AND NULL GENERALIZED MOTZKIN SEQUENCE SPACES(Ele-Math, 2025) Erdem, Sezer; Şahin, Adem; Demiriz, SerkanThe BK sequence spaces c(G) and c0 (G) generated by generalized Motzkin (GM) matrix G are constructing in this study. The Schauder bases of these spaces are obtained and the inclusion relations are presented. Additionally, the α-, β-andγ-duals of c(G) and c0 (G) are determined and finally, the necessary and sufficient conditions for a matrix to be in the class of matrices containing new spaces are explored. © Zagreb.Öğe On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences(Emrah Evren KARA, 2025) Erdem, Sezer; Demiriz, SerkanThe primary objective of this study is to construct a novel double sequence space by utilizing the domain of a 4-dimensional (4D) matrix in the space ℒu of the absolutely summable double sequences defined via the well-known Catalan numbers. Within this framework, various algebraic and topological properties of the newly introduced space are investigated. The study further aims to compute the α-, β (bp)-, and γ-duals of the space. Another essential part of the research involves characterizing certain classes of matrix transformations from the newly defined space to some classical double sequence spaces and vice versa. These contributions are expected to enrich the theory of sequence spaces and matrix transformations by introducing new insights based on special integer sequences. © (2026). All right reserved.Öğe ON THE JORDAN-TYPE SEQUENCE SPACES WHICH INCLUDE THE SPACES c AND c0 AND COMPACT OPERATORS(Springer, 2026) Bilgin Ellidokuzoğlu, Hacer; Erdem, Sezer; Demiriz, Serkan; İlkhan Kara, MerveIn this study, novel sequence spaces are introduced as the domains of the Jordan-type matrix operator within the spaces of c and c0. Initially, these new spaces are defined, and their fundamental properties, including completeness and other topological characteristics, are examined. Furthermore, the existence of a Schauder basis for these spaces is established, highlighting its crucial role in their structural analysis. Next, the α-, β-, and γ-duals of the newly constructed sequence spaces are determined to provide a deeper understanding of their duality relations. Subsequently, the classes of infinite matrices that map sequences from these new spaces into classical sequence spaces, such as ℓp, ℓ∞, c, and c0, are characterized, along with the reverse transformations. Finally, attention is given to compact operators acting on these spaces, and a comprehensive characterization of their behavior is provided. Necessary and sufficient conditions for compactness are explored, and their implications in functional analysis are discussed. © The Author(s) 2026.Öğe Oresme Numbers and Associated BK-Sequence Spaces(Springer Int Publ Ag, 2025) Erdem, Sezer; Demiriz, SerkanThe aim of this research is to present the formulation of a new conservative matrix operator containing non-integer Oresme numbers, to obtain new BK-sequence spaces with the help of domains of this matrix operator on the spaces of convergent and null sequences. In the continuation of study, inclusion relations, alpha, beta and gamma duals, Schauder basis and matrix mapping classes concerning these spaces are introduced. Finally, compact operators on these novel sequence spaces are characterized by the utilization of Hausdorff measure of non-compactness.Öğe q-Cesaro double sequence space (L)over-tildesq derived by q-analog(Sciendo, 2023) Erdem, Sezer; Demiriz, SerkanThis study includes the new Banach space (L) over tilde (q)(s) designed as the domain in Ls space of the 4d (4-dimensional) q-Cesaro matrix obtained as the q-analog of the well-known 4d Cesaro matrix. After showing the completeness of the aforementioned space, giving some inclusion relations, determining the fundamental set of this space and calculating the duals, finally, some matrix transformations related to the new space were characterized.Öğe Some topological and geometric properties of novel generalized Motzkin sequence spaces(Springer-Verlag Italia Srl, 2025) Demiriz, Serkan; Sahin, Adem; Erdem, SezerThe present study aims constructing the BK-spaces l(p)(G)and l(infinity)(G)generated by generalized Motzkin (GM) matrix G, which is conservative and derived by GM numbers. The Schauder basis of l(p)(G)for 1 <= p < infinity is obtained and the inclusion relations are presented. Additionally, the alpha-,beta-and gamma-duals of l(p)(G)and l(infinity) (G)are described and finally, these spaces are examined in terms of some topological and geometric properties.Öğe The New Hahn Sequence Space via $(p,q)$-Calculus(Emrah Evren KARA, 2025) Ellidokuzoğlu, Hacer Bilgin; Erdem, Sezer; Demiriz, Serkan[Abstract Not Available]
