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On Lacunary strong σ-convergence with respect to a sequence of φ-fuctions

Başarir M.

Fasciculi Mathematici

2010

Nr 43

19-32

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.

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

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.

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

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.

Boundedness of superposition operators on some sequence spaces defined by moduli

Molder A.

Demonstratio Mathematica

2006

Vol. 39, nr 4

869-886

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.

Vector-valued FK-spaces defined by a modulus function

Yilmaz Y., Solak I.

Demonstratio Mathematica

2005

Vol. 38, nr 3

633--640

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.