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1
Content available remote Some new generalized Riesz spaces over modulus function
Gupkari Sameer Ahmad
Fasciculi Mathematici
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2023
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nr 66
39--47
EN
The structure of this paper is to introduce the new sequence space of Riesz type of the form rqF(△ps) by using modulus function. We will prove that it is complete linear paranormed space. It will be shown to be linearly isomorphism with ℓ(p). Further, some inclusion relation will be computed.
2
Content available remote On some I-convergent double sequence spaces of fuzzy real numbers defined by modulus function
Das M.
Fasciculi Mathematici
|
2015
|
Nr 55
19--28
EN
In this article our aim to introduce some new I-convergent double sequence spaces of fuzzy real numbers defined by modulus function and studies their some topological and algebraic properties. Also we establish some inclusion relations.
3
Content available remote On generalized Orlicz sequence spaces defined by double sequences
Kolk E.
Fasciculi Mathematici
|
2015
|
Nr 55
65--80
EN
S.D. Parashar and B. Choudhary defined in 1994 certain paranorms for some Orlicz sequence spaces. Their ideas are applied later for topologization of various generalized Orlicz sequence spaces. The author determines in 2011 some alternative F-seminorms (which are also paranorms) for such spaces. In this paper these results are extended to generalized Orlicz sequence spaces defined via double sequences.
4
Content available remote Some generalized spaces of vector valued double sequences defined by a modulus
Subramanian N.
Fasciculi Mathematici
|
2013
|
Nr 51
159--172
EN
In this paper we generalize the xf2 by introducing the sequence space xfmn2 (Δ(ηϒ)μ,p,q,r) and exhibit some general properties of the space.
5
Content available remote On Cesàro sequence space defined by a modulus function
Bala I.
Demonstratio Mathematica
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2013
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Vol. 46, nr 1
157--163
EN
The object of this paper is to introduce the sequence space ces(f, p) using a modulus function f. Various algebraic and topological properties of this space, and certain inclusion relations have been discussed which generalize several known results of Shiue [10], Sanhan and Suantai [9], and Leibowitz [2].
6
Content available remote A Novel Steganographic Method with Four-Pixel Differencing and Modulus Function
Xin Liao Xin, Qiaoyan Wen Qiaoyan, Zeli Zhao Zeli, Jie Zhang Jie
Fundamenta Informaticae
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2012
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Vol. 118, nr 3
281-289
EN
To improve the stego-image quality and provide a larger embedding capacity, a novel steganographic method based on four-pixel differencing and modulus function is presented. We process a block of four neighboring pixels, and form three two-pixel groups to record the information of secret data. In each group, the difference value between two pixels is exploited to estimate how many secret bits will be embedded. Two pixels will be adjusted so that the sum of the remainders of them is equal to secret data. In order to extract the secret data exactly, four pixel values in a block are adjusted synchronously by using modulus function. An optimization problem is formulated to minimize the embedding distortion. A theoretical proof is given to ensure the solvability of the problem. The experimental results show the proposed method not only has a larger embedding capacity but also provides better stego-image quality.
7
Content available remote On Lacunary strong σ-convergence with respect to a sequence of φ-fuctions
Başarir M.
Fasciculi Mathematici
|
2010
|
Nr 43
19-32
EN
In this paper, we introduce some new sequence spaces combining with lacunary sequence, σ-convergence, a sequence of φ-functions and a sequence of modulus functions. We establish some inclusion relations between these spaces under some conditions. Also we studied connections between lacunary (A, φk, σ )-statistically convergence with these spaces.
8
Content available remote Certain spaces of sequences of fuzzy numbers defined by a modulus function
Talo O., Basar F.
Demonstratio Mathematica
|
2010
|
Vol. 43, nr 1
139-149
EN
The main purpose of the present paper is to introduce the spaces l infinity (F, f), c(F, f), co(F, f) and lp(F, f, s) of sequences of fuzzy numbers defined by a modulus function. Furthermore, some inclusion theorems related to these sets are given and shown that l infinity(Ff), co F,f) and Lp(FJ,s) are solid.
9
Content available remote On some generalized new type difference sequence spaces defined by a modulus function in a seminformed space
Esi A., Tripathy B. C.
Fasciculi Mathematici
|
2008
|
Nr 40
15-24
EN
The idea of difference sequence spaces were introduced by Kizmaz [6] and generalized by Et. and Colak [4]. Later Tripathy, Esi and Tripathy [15] introduced the notion of the new difference operator Δnm for n, m ∈ N. In this paper we introduced some new type of generalized difference sequence spaces defined by a modulus function and the new type of statistically convergent generalized difference sequence space. We study their different properties and obtain some inclusion relations involving these new type difference sequence spaces.
10
Content available remote Strong invariant A-summability with respect to a sequence of modulus functions in seminormed space
Bhardwaj V., Bala I.
Demonstratio Mathematica
|
2008
|
Vol. 41, nr 4
869-877
EN
The object of this paper is to introduce some new strongly invariant A-summable sequence spaces defined by a sequence of modulus functions T = (fk) in a seminormed space, when A = (ank) is a non-negative regular matrix. Various algebraic and topological properties of these spaces, and some inclusion relations between these spaces have been discussed. Finally, we study some relations between ^4-invariant statisti-cal convergence and strong invariant A-summability with respect to a seąuence of modulus functions in a seminormed space.
11
Content available remote Statistical convergence on composite vector valued sequence space
Basu A., Srivastava P. D.
Journal of Mathematics and Applications
|
2007
|
Vol. 29
75-90
EN
In this paper, we have defined the idea of statistical convergence and statistically Cauchy sequence over the generalized class of composite vector valued sequence space F(Ek, f). The class F(Ek, f) is in-troduced and discussed by Ghosh and Srivastava [7], where F is a normal paranormed sequence space, Ek's are Banach spaces and f is a modulus function. We have established some results of Fridy, Connor and Rath and Tripathy, such as, decomposition of statistically convergent sequences, equivalence of statistical convergence and statistical Cauchy convergence and sequentially completeness of the space of bounded statistically con-vergent sequences of F [E, f].
12
Content available remote Boundedness of superposition operators on some sequence spaces defined by moduli
Molder A.
Demonstratio Mathematica
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2006
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Vol. 39, nr 4
869-886
EN
For a solid sequence space lambda and a sequence of modulus functions fi = (phik) let lambda(fi) = {x = (xk) : (phik(|xk|)) is an element of lambda}. Provided another solid sequence space ž and a sequence of modulus functions psi= psi(k), we give necessary and sufficient conditions for the local boundedness and boundedness of superposition operators Pf from lambda(fi)) into ž(psi) for some Banach sequence spaces lambda and ž under the assumptions that topologies on the sequence spaces lambda(fi) and ž(psi) are given by certain F-norms. As applications we characterize bounded superposition operators on some multiplier sequence spaces of Maddox type.
13
Content available remote Vector-valued FK-spaces defined by a modulus function
Yilmaz Y., Solak I.
Demonstratio Mathematica
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2005
|
Vol. 38, nr 3
633--640
EN
We introduced and investigated the sequence space lambda (Xk,r,f,s) defined by a modulus function f, and constructed its FK-structure under some conditions. Also we exposed some inclusion relations among the variations of the space.
14
Content available remote Lacunary strong Ap-convergence with respect to a modulus
Bilgin T.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2001
|
[Z] 41
51-57
EN
The definition of lacunary strong A-convergence with respect to a modulus is extended to a definition of lacunary strong Ap-convergence with respect to a modulus when p = (p_i) is a real sequence with positive terms. We study some connections between lacunary strong Ap-convergence with respect to a modulus and lacunary A-statistical convergence.
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