Acta mathematica scientia, Series B >
ON THE mth ORDER DIFFERENCE SEQUENCE SPACE OF GENERALIZED WEIGHTED MEAN AND COMPACT OPERATORS
Received date: 2012-01-17
Revised date: 2012-08-09
Online published: 2013-05-20
In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space ?(u, v, p; Δ(m)), which consist of the sequences whose generalized weighted Δ(m)-difference means are in the linear space ?(p) defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from ?(u, v, p,Δ(m)) to ?∞, c, and c0. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space ?p(u, v, Δ(m)) (1≤p < 1).
Metin BASARIR , Emrah Evren KARA . ON THE mth ORDER DIFFERENCE SEQUENCE SPACE OF GENERALIZED WEIGHTED MEAN AND COMPACT OPERATORS[J]. Acta mathematica scientia, Series B, 2013 , 33(3) : 797 -813 . DOI: 10.1016/S0252-9602(13)60039-9
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