scholarly journals Some properties of Generalized Fibonacci difference bounded and $p$-absolutely convergent sequences

2018 ◽  
Vol 36 (1) ◽  
pp. 37 ◽  
Author(s):  
Bipan Hazarika ◽  
Anupam Das
Keyword(s):  
Sequence Space ◽  
Geometric Properties ◽  
Matrix Classes ◽  
Band Matrix ◽  
Inclusion Relations ◽  
Alpha Beta ◽  
Convergent Sequences

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 its $\alpha-,\beta-,\gamma-$duals. We also characterize some matrix classes on the space $l_{p}(\hat{F}(r,s))$ and examine some geometric properties of this space.

scholarly journals Matrix transformation of Fibonacci band matrix on generalized $bv$-space and its dual spaces

2018 ◽  
Vol 36 (3) ◽  
pp. 41-52 ◽  
Author(s):  
Anupam Das ◽  
Bipan Hazarika
Keyword(s):  
Sequence Space ◽  
Matrix Transformation ◽  
Matrix Classes ◽  
Band Matrix ◽  
Dual Spaces ◽  
Inclusion Relations ◽  
Alpha Beta

In this paper we introduce a new sequence space $bv(\hat{F})$ by using the Fibonacci band matrix $\hat{F}.$ We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. Finally we characterize some matrix classes on the space $bv(\hat{F}).$

scholarly journals Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spacesℓpandℓ∞

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Feyzi Başar ◽  
Ali Karaisa
Keyword(s):  
Sequence Space ◽  
Normed Space ◽  
Geometric Properties ◽  
Modulus Of Convexity ◽  
Inclusion Relations ◽  
Alpha Beta

We introduce the sequence spaceℓpλ(B)of none absolute type which is ap-normed space andBKspace in the cases0<p<1and1⩽p⩽∞, respectively, and prove thatℓpλ(B)andℓpare linearly isomorphic for0<p⩽∞. Furthermore, we give some inclusion relations concerning the spaceℓpλ(B)and we construct the basis for the spaceℓpλ(B), where1⩽p<∞. Furthermore, we determine the alpha-, beta- and gamma-duals of the spaceℓpλ(B)for1⩽p⩽∞. Finally, we investigate some geometric properties concerning Banach-Saks typepand give Gurarii's modulus of convexity for the normed spaceℓpλ(B).

scholarly journals A new perspective on paranormed Riesz sequence space of non-absolute type

2015 ◽  
Vol 3 (4) ◽  
pp. 150 ◽  
Author(s):  
Murat Candan
Keyword(s):  
Sequence Space ◽  
Topological Properties ◽  
Real Numbers ◽  
Positive Real ◽  
Band Matrix ◽  
Current Article ◽  
Matrix Class ◽  
Alpha Beta ◽  
New Perspective ◽  
Convergent Sequences

<p>The current article mainly dwells on introducing Riesz sequence space \(r^{q}(\widetilde{B}_{u}^{p})\) which generalized the prior studies of Candan and Güneş [28], Candan and Kılınç [30]  and consists of all sequences whose \(R_{u}^{q}\widetilde{B}\)-transforms are in the space \(\ell(p)\), where \(\widetilde{B}=B(r_{n},s_{n})\) stands for double sequential band matrix \((r_{n})^{\infty}_{n=0}\) and \((s_{n})^{\infty}_{n=0}\) are given convergent sequences of positive real numbers. Some topological properties of the new brand sequence space have been investigated as well as \(\alpha\)- \(\beta\)-and \(\gamma\)-duals. Additionally, we have also constructed the basis of \(r^{q}(\widetilde{B}_{u}^{p})\). Eventually, we characterize a matrix class on the sequence space. These results are more general and more comprehensive than the corresponding results in the literature.</p>

scholarly journals Domain of the Double Sequential Band Matrix in the Sequence Space

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Havva Nergiz ◽  
Feyzi Başar
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Matrix Transformations ◽  
Difference Matrix ◽  
Band Matrix ◽  
Alpha Beta

The sequence space was introduced by Maddox (1967). Quite recently, the domain of the generalized difference matrix in the sequence space has been investigated by Kirişçi and Başar (2010). In the present paper, the sequence space of nonabsolute type has been studied which is the domain of the generalized difference matrix in the sequence space . Furthermore, the alpha-, beta-, and gamma-duals of the space have been determined, and the Schauder basis has been given. The classes of matrix transformations from the space to the spaces ,candc0have been characterized. Additionally, the characterizations of some other matrix transformations from the space to the Euler, Riesz, difference, and so forth sequence spaces have been obtained by means of a given lemma. The last section of the paper has been devoted to conclusion.

scholarly journals Some Topological and Geometric Properties of Some New Spaces ofλ-Convergent and Bounded Series

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Meltem Kaya ◽  
Hasan Furkan
Keyword(s):  
Fixed Point ◽  
Convexity Property ◽  
Point Property ◽  
Geometric Properties ◽  
Matrix Classes ◽  
Modulus Of Convexity ◽  
Opial Property ◽  
Weak Fixed Point Property ◽  
Inclusion Relations ◽  
Schauder Bases

The main purpose of this study is to introduce the spacescsλ,cs0λ, andbsλwhich areBK-spaces of nonabsolute type. We prove that these spaces are linearly isomorphic to the spacescs,cs0, andbs, respectively, and derive some inclusion relations. Additionally, Schauder bases of the spacescsλandcs0λhave been constructed and theα-,β-, andγ-duals of these spaces have been computed. Besides, we characterize some matrix classes from the spacescsλ,cs0λ, andbsλto the spaceslp,c, andc0, where1≤p≤∞. Finally, we examine some geometric properties of these spaces as Gurarǐ’s modulus of convexity, propertym∞, property(M), property WORTH, nonstrict Opial property, and weak fixed point property.

scholarly journals On the Paranormed Nörlund Sequence Space of Nonabsolute Type

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Sequence Space ◽  
Infinite Matrices ◽  
Geometric Properties ◽  
Alpha Beta

Maddox defined the spaceℓ(p)of the sequencesx=(xk)such that∑k=0∞‍|xk|pk<∞, in Maddox, 1967. In the present paper, the Nörlund sequence spaceNt(p)of nonabsolute type is introduced and proved that the spacesNt(p)andℓ(p)are linearly isomorphic. Besides this, the alpha-, beta-, and gamma-duals of the spaceNt(p)are computed and the basis of the spaceNt(p)is constructed. The classes(Nt(p):μ)and(μ:Nt(p))of infinite matrices are characterized. Finally, some geometric properties of the spaceNt(p)are investigated.

scholarly journals SOME GENERALIZED FIBONACCI DIFFERENCE SPACES DEFINED BY A SEQUENCE OF MODULUS FUNCTIONS

2017 ◽  
pp. 095 ◽  
Author(s):  
Gülsen Kılınç ◽  
Murat Candan
Keyword(s):  
Real Number ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Inclusion Relations ◽  
Alpha Beta

This paper submits the sequence space $l\left( \widehat{F}\left( r,s\right),\mathcal{F},p,u\right) $ and $l_{\infty }\left( \widehat{F}\left(r,s\right) ,\mathcal{F},p,u\right) $of non-absolute type under the domain ofthe matrix$\widehat{\text{ }F}\left( r,s\right) $ constituted by usingFibonacci sequence and non-zero real number $r$, $s$ and a sequence ofmodulus functions. We study some inclusion relations, topological andgeometric properties of these spaceses. Further, we give the $\alpha $- $%\beta $- and $\gamma $-duals of said sequence spaces and characterization ofthe classes $\left( l\left( \widehat{F}\left( r,s\right) ,\mathcal{F}%,p,u\right) ,X\right) $ and $\left( l_{\infty }\left( \widehat{F}\left(r,s\right) ,\mathcal{F},p,u\right) ,X\right) $.

scholarly journals Some Geometric Properties of the Domain of the Double Sequential Band Matrix in the Sequence Space

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Havva Nergiz ◽  
Feyzi Başar
Keyword(s):  
Sequence Space ◽  
Geometric Properties ◽  
Band Matrix

The sequence space was introduced by Maddox (1967). Quite recently, the sequence space of nonabsolute type has been introduced and studied which is the domain of the double sequential band matrix in the sequence space by Nergiz and Başar (2012). The main purpose of this paper is to investigate the geometric properties of the space , like rotundity and Kadec-Klee and the uniform Opial properties. The last section of the paper is devoted to the conclusion.

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