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 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 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 On the paranormed space $\mathcal{M}_{u}(t)$ of double sequences

2017 ◽  
Vol 37 (3) ◽  
pp. 99-111 ◽  
Author(s):  
Feyzi Başar ◽  
Hüsamettin Çapan
Keyword(s):  
Sequence Space ◽  
Normed Space ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Double Sequences ◽  
Paranormed Space ◽  
Dual Spaces ◽  
Dimensional Matrix ◽  
Paranormed Sequence Space ◽  
Alpha Beta

In this paper, we introduce the paranormed sequence space $\mathcal{M}_{u}(t)$ corresponding to the normed space $\mathcal{M}_{u}$ of bounded double sequences. We examine general topological properties of this space and determine its alpha-, beta- and gamma-duals. Furthermore, we characterize some classes of four-dimensional matrix transformations concerning this space and its dual spaces.

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 On some new sequence spaces of non-absolute type related to the spaces ℓp and ℓ∞ I

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 33-51 ◽  
Author(s):  
M. Mursaleen ◽  
Abdullah Noman
Keyword(s):  
Sequence Space ◽  
Normed Space ◽  
Sequence Spaces ◽  
Inclusion Relations ◽  
Bk Space

In the present paper, we introduce the sequence space l?p of non-absolute type and prove that the spaces ??p and lp are linearly isomorphic for 0 < p ? ?. Further, we show that ??p is a p-normed space and a BK-space in the cases of 0 < p < 1 and 1 ? p ? ?, respectively. Furthermore, we derive some inclusion relations concerning the space ??p. Finally, we construct the basis for the space ??p, where 1 ? p < ?.

scholarly journals Someℓ(p)-Type New Sequence Spaces and Their Geometric Properties

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Ekrem Savaş ◽  
Vatan Karakaya ◽  
Necip Şimşek
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Geometric Properties ◽  
Modulus Of Convexity ◽  
P Type

We introduce anℓ(p)-type new sequence space and investigate its some topological properties includingAKandADproperties. Besides, we examine some geometric properties of this space concerning Banach-Saks typepand Gurarii's modulus of convexity.

scholarly journals Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator

2021 ◽  
Vol 19 (1) ◽  
pp. 329-337
Author(s):  
Huo Tang ◽  
Kaliappan Vijaya ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Analytic Function ◽  
Differential Operator ◽  
Lower Bounds ◽  
Analytic Functions ◽  
Function Class ◽  
Partial Sums ◽  
Generalized Function ◽  
Inclusion Relations ◽  
Alpha Beta

Abstract Let f k ( z ) = z + ∑ n = 2 k a n z n {f}_{k}\left(z)=z+{\sum }_{n=2}^{k}{a}_{n}{z}^{n} be the sequence of partial sums of the analytic function f ( z ) = z + ∑ n = 2 ∞ a n z n f\left(z)=z+{\sum }_{n=2}^{\infty }{a}_{n}{z}^{n} . In this paper, we determine sharp lower bounds for Re { f ( z ) / f k ( z ) } {\rm{Re}}\{f\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}\left(z)\} , Re { f k ( z ) / f ( z ) } {\rm{Re}}\{{f}_{k}\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}f\left(z)\} , Re { f ′ ( z ) / f k ′ ( z ) } {\rm{Re}}\{{f}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}^{^{\prime} }\left(z)\} and Re { f k ′ ( z ) / f ′ ( z ) } {\rm{Re}}\{{f}_{k}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}^{^{\prime} }\left(z)\} , where f ( z ) f\left(z) belongs to the subclass J p , q m ( μ , α , β ) {{\mathcal{J}}}_{p,q}^{m}\left(\mu ,\alpha ,\beta ) of analytic functions, defined by Sălăgean ( p , q ) \left(p,q) -differential operator. In addition, the inclusion relations involving N δ ( e ) {N}_{\delta }\left(e) of this generalized function class are considered.

scholarly journals Dual pairs of sequence spaces

2001 ◽  
Vol 28 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Johann Boos ◽  
Toivo Leiger
Keyword(s):  
Sequence Space ◽  
Dual Pair ◽  
General Concept ◽  
Sequence Spaces ◽  
Dual Pairs ◽  
The Third ◽  
Convex Sequence ◽  
Starting Point ◽  
Alpha Beta ◽  
Locally Convex

The paper aims to develop for sequence spacesEa general concept for reconciling certain results, for example inclusion theorems, concerning generalizations of the Köthe-Toeplitz dualsE×(×∈{α,β})combined with dualities(E,G),G⊂E×, and theSAK-property (weak sectional convergence). TakingEβ:={(yk)∈ω:=𝕜ℕ|(ykxk)∈cs}=:Ecs, wherecsdenotes the set of all summable sequences, as a starting point, then we get a general substitute ofEcsby replacingcsby any locally convex sequence spaceSwith sums∈S′(in particular, a sum space) as defined by Ruckle (1970). This idea provides a dual pair(E,ES)of sequence spaces and gives rise for a generalization of the solid topology and for the investigation of the continuity of quasi-matrix maps relative to topologies of the duality(E,Eβ). That research is the basis for general versions of three types of inclusion theorems: two of them are originally due to Bennett and Kalton (1973) and generalized by the authors (see Boos and Leiger (1993 and 1997)), and the third was done by Große-Erdmann (1992). Finally, the generalizations, carried out in this paper, are justified by four applications with results around different kinds of Köthe-Toeplitz duals and related section properties.

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