Related papers: Some New Paranormed Difference Sequence Spaces Der…
In this study, we define new paranormed sequence spaces by combining a double sequential band matrix and a diagonal matrix. Furthermore, we compute the $\alpha-,\beta-$ and $\gamma-$ duals and obtain bases for these sequence spaces. Besides…
In the present paper, by using the band matrix F defined by the Fibonacci sequence, we introduce the sequence sequence spaces c_0(F) and c(F). Also, we give some inclusion relations and construct the bases of the spaces c_0(F) and c(F).…
In this work, we introduce some new generalized sequence space related to the space l(p). Furthermore we investigate some topological properties as the completeness, the isomorphism and also we give some inclusion relations between this…
This paper presents new sequence spaces $X(r, s, t, p ;\Delta)$ for $X \in \{l_\infty(p), c(p), c_0(p), l(p)\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete under a suitable…
In this work, we define new sequence spaces by combining generalized weighted mean and difference operator. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the alpha, beta…
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…
In this study, we define a new triangle matrix $\hat{W}=\{w_{nk}^{\lambda}(r,s,t)\}$ which derived by using multiplication of $\lambda=(\lambda_{nk})$ triangle matrix with $B(r,s,t)$ triple band matrix. Also, we introduce the sequence…
This paper deals with new sequence spaces $X(r, s, t ;\Delta) $ for $X\in \{l_\infty, c, c_0\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete normed linear spaces and the spaces $X(r,…
Let $\Delta^{(\alpha)}$ denote the fractional difference operator. In this paper, we define new difference sequence spaces $c_0(\Gamma,\Delta^{(\alpha)},u)$ and $c(\Gamma,\Delta^{(\alpha)},u)$. Also, the $\beta-$ dual of the spaces…
The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$ We also establish a few inclusion relations concerning this space and determine…
The aim of the paper is to introduced the spaces $c_{0}^{\lambda}(\hat{F})$ and $c^{\lambda}(\hat{F})$ which are the BK-spaces of non-absolute type and also derive some inclusion relations. Further, we determine the…
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…
In this paper, we connect two well established theories, the Fibonacci numbers and the Jordan algebras. We give a series of matrices, from literature, used to obtain recurrence relations of second-order and polynomial sequences. We also…
In this paper, we define the bi-periodic Fibonacci matrix sequence that represent bi-periodic Fibonacci numbers. Then, we investigate generating function, Binet formula and summations of bi-periodic Fibonacci matrix sequence. After that, we…
The research aims to construct a new type of matrix called the Fibonacci-Hessenberg-Lorentz matrix by multiplying Fibonacci-Hessenberg matrices with Lorentz matrix multiplication. The study will start by examining the properties of…
In this paper, we introduce some new double sequence spaces $\mathcal{M}_u(\Delta)$ and $\mathcal{C}_{\vartheta}(\Delta)$, where $\vartheta\in\{bp,bp0,r,r0\}$ as the domains of the four-dimensional forward difference matrix in the double…
We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial summation, polynomial identities and binomial…
The aim of the paper is to introduce the spaces $\ell_{\infty}^{\lambda}(\widehat{F})$ and $\ell_{p}^{\lambda}(\widehat{F})$ derived by the composition of the two infinite matrices $\Lambda=(\lambda_{nk})$ and $\widehat{F}=\left( f_{nk}…
The main purpose of this article is to introduce some new binomial difference sequence spaces of fractional order ${\tilde{\alpha}} $ along with infinite matrices. Some topological properties of these spaces are considered along with the…
We present some new linear, quadratic, cubic and quartic binomial Fibonacci, Lucas and Fibonacci--Lucas summation identities.