Mikail Et

On Some New Generalized Difference Sequence Spaces

In this paper we introduce some generalized difference sequence spaces and investigate inclusion relations and Köthe-Toeplitz duals.

Generalized difference sequence spaces on seminormed space defined by Orlicz functions

In this paper we define the sequence space ℓM (Δm, p, q, s) on a seminormed complex linear space by using an Orlicz function. We study its different algebraic and topological properties like solidness, symmetricity, monotonicity, convergence free etc. We prove some inclusion relations involving ℓM (Δm, p, q, s).

λ-Difference sequence spaces of fuzzy numbers

In this paper, using the difference operator of order m and an Orlicz function, we introduce and examine some classes of sequences of fuzzy numbers. We give the relations between the strongly Cesaro type convergence and statistical convergence in these spaces. Furthermore, we study some of their properties like completeness, solidity, symmetricity, etc. We also give some inclusion relations related to these classes.

Some Geometric Inequalities in a New Banach Sequence Space

The difference sequence space, which is a generalization of the space introduced and studied by Sargent (1960), was defined by Çolak and Et (2005). In this paper we establish some geometric inequalities for this space.

On λ-statistical convergence of order α of sequences of function

In this study we introduce the concept of Sλα(f)-statistical convergence of sequences of real valued functions. Also some relations between Sλα(f)-statistical convergence and strong wλpβ(f)-summability are given.MSC:40A05, 40C05, 46A45.

Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers

The purpose of this paper is to introduce the concepts of almost lacunary statistical convergence and strongly almost lacunary convergence of sequences of fuzzy numbers. We give some relations related to these concepts. We establish some connections between strongly almost lacunary convergence and almost lacunary statistical convergence of sequences of fuzzy numbers. It is also shown that if a sequence of fuzzy numbers is strongly almost lacunary convergent with respect to an Orlicz function then it is almost lacunary statistical convergent.

On(Δm,I)-Statistical Convergence of Orderα

The idea of I-convergence of real sequences was introduced by Kostyrko et al., (2000/01) and also independently by Nuray and Ruckle (2000). In this paper, we introduce the concepts of (Δm, I)-statistical convergence of order α and strong (Δp m, I)-Cesàro summability of order α of real sequences and investigated their relationship.

On pointwise and uniform statistical convergence of order α for sequences of functions

In this paper, we introduce the concepts of pointwise and uniform statistical convergence of order α for sequences of real-valued functions. Furthermore, we give the concept of an α-statistically Cauchy sequence for sequences of real-valued functions and prove that it is equivalent to pointwise statistical convergence of order α for sequences of real-valued functions. Also, some relations between Sα(f)-statistical convergence and strong wpβ(f)-summability are given.MSC:40A05, 40C05, 46A45.

On λ-statistical convergence and strongly λ-summable functions of order α

In this study, using the notion of (V,λ)-summability and λ-statistical convergence, we introduce the concepts of strong (V,λ,p)-summability and λ-statistical convergence of order α of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,∞). Also some relations between λ-statistical convergence of order α and strong (V,λ,p)-summability of order β are given.MSC:40A05, 40C05, 46A45.

On pα-dual spaces of generalized difference sequence spaces

Abstract In this paper, we compute the p α -, p β - and p γ -duals of the sequence spaces l ∞ ( k m ) , c ( k m ) , c 0 ( k m ) , the p N -dual of the sequence spaces Δ v , r m ( l ∞ ) , Δ v , r m ( c ) and the p α -dual of the sequence spaces Δ v , r m ( l ∞ ) , Δ v , r m ( c ) and Δ v , r m ( c 0 ) .