Mahmut Işık

Strongly almost (ω, λ, q)-summable sequences

The purpose of this paper is to introduce the spaces of sequences that are strongly almost (ω, λ, q)-summable with respect to a modulus function. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly (ω, λ, q)-summable with respect to a modulus function, then it is S(λq)-statistically convergent.

Generalized Vector-Valued Sequence Spaces Defined by Modulus Functions

We introduce the vector-valued sequence spaces , , and , and , using a sequence of modulus functions and the multiplier sequence of nonzero complex numbers. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly -Cesàro summable with respect to the modulus function then it is -statistically convergent.

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 ) .

Δim–lacunary statistical convergence of order α

The purpose of this work is to introduce the concepts of Δim–lacunary statistical convergence of order α and lacunary strongly (Δim,p)–convergence of order α. We establish some connections between lacunary strongly (Δim,p)–convergence of order α and Δim–lacunary statistical convergence of order α. It is shown that if a sequence is lacunary strongly (Δim,p)–summable of order α then it is Δim–lacunary statistically convergent of order α.

Some properties of the sequence space

In this paper we define the sequence space on a seminormed complex linear space by using an Orlicz function. We give various properties and some inclusion relations on this space.MSC:40A05, 40C05, 40D05.

Statistical convergence of order β for double sequences of fuzzy numbers defined by a modulus function

In the present paper, we extend the notions of statistically convergence of order β and strong Cesaro summability of order β for sequences of fuzzy numbers and introduce the notions of f–statistically convergence of order β and strong Cesaro summability of order β for β ∈ (0, 1] with respect to an unbounded modulus function f for double sequences of fuzzy numbers and give some inclusion theorems.

f–lacunary statistical convergence of order (α, β)

The main purpose of this paper is to introduce the concepts of f–lacunary statistical convergence of order (α, β) and strong f–lacunary summability of order (α, β) of sequences of real numbers for 0 <α ≤ β ≤ 1, where f is an unbounded modulus.

Almost -Statistical and Strongly Almost -Convergence ofOrder of Sequences of Fuzzy Numbers

The main purpose of this article is to introduce the concepts of almost -statistical convergence and strongly almost -convergence of order of sequences of fuzzy numbers with respect to an Orlicz function. We give some relations between strongly almost -convergence and almost -statistical convergence of order of sequences of fuzzy numbers.

Recent Developments on Summability Theory and Its Applications

1Department of Mathematics, Firat University, 23119 Elazig, Turkey 2Department of Mathematics, Siirt University, 56100 Siirt, Turkey 3Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India 4Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia 5Faculty of Education, Harran University, Osmanbey Campus, 63190 Şanliurfa, Turkey 6Department of Mathematics, Ohio University, Athens, OH 45701, USA 7Department of Mathematics, Faculty of Arts and Sciences, Fatih University, Hadimkoy Campus, Buyukcekmece, 34500 Istanbul, Turkey