I-convergent sequence spaces associated with multiplier sequences

Abstract

Abstract. In this article we introduce the sequence spaces c I (Λ) , c I 0 (Λ) , m I (Λ) and m I 0 (Λ) associated with the multiplier sequence Λ = (λ k ) of non-zero scalars. We study the different algebraic and topological properties of these sequence spaces like solidness, symmetricity, sequence algebra, convergence free etc. Also we characterize the multiplier problem and obtain some inclusion relation involving these sequence spaces.Mathematics subject classification (2000): 40A05, 40C05.

The ∫ 𝚪𝟐𝝀𝑰 statistical convergence of real numbers over Musielak 𝒑-metric space

“…The notion of deal convergence was introduced first by Kostyrko et al (2000) as a generalization of statistical convergence which was further studied in toplogical spaces by Kumar (2007) and Kumar and Kumar (2008), and also more applications of ideals can be deals with various authors by Hazarika (2009Hazarika ( , 2012aHazarika ( ,b,c, 2013aHazarika ( ,b, 2014a, Savas (2011), Hazarika et al (2014), Hazarika and Kumar (2014), Tripathy and Hazarika (2008, 2009. While an admissible ideal I of Y further satisfies {x} ∈ I for each x ∈ Y.…”

On a class of n-normed sequences related to $\ell_p$-space

“…In the recent past different classes of sequences have been introduced and their different algebraic and topological properties have been investigated by Altin, Et and Tripathy [1], Tripathy [14], Tripathy and Dutta [15,16], Tripathy and Hazarika [17,18], Tripathy and Mahanta [20,21,22], Tripathy and Sarma [23], Tripathy and Sen [25] and many others.…”

“…Later on it was studied from the sequence space point of view and some matrix classes were characterized with one member as m(φ) by Esi [5], Et, Altin and Altinok [6], Fistikci, Acikgoz and Esi [7], Rath and Tripathy [11], Tripathy [13], Tripathy and Sen [24], Tripathy and Mahanta [17] and many others. In this article we introduce the n-normed space (m(φ), ... n ) and investigate its different algebraic and topological properties.…”

Lacunary I-Convergent Sequences

“…Later on it was studied by Demirci [1], Salat, Tripathy and Ziman ( [8], [9]), Tripathy and Hazarika ( [14], [15], [16], [17]), Tripathy and Mahanta [19], Tripathy and Sarma [21] and many others.…”