ON THE mth ORDER DIFFERENCE SEQUENCE SPACE OF GENERALIZED WEIGHTED MEAN AND COMPACT OPERATORS

doi:10.1016/S0252-9602(13)60039-9

Abstract

Abstract:

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).

Key words: Paranormed sequence spaces, difference sequence spaces, weighted mean, α-, β-, γ-duals, matrix mappings, Hausdorff measure of noncompactness, compact operators

CLC Number:

46A45

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.

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