Measure of noncompactness of matrix operators on some difference sequence spaces of weighted means

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Mursaleen M., KARAKAYA V., Polat H., ŞİMŞEK N.

Computers and Mathematics with Applications, cilt.62, sa.2, ss.814-820, 2011 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 62 Sayı: 2
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.camwa.2011.06.011
  • Dergi Adı: Computers and Mathematics with Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.814-820
  • Anahtar Kelimeler: Sequence space, Weighted mean, Matrix transformation, Compact operator, Hausdorff measure of noncompactness
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

For a sequence x=(xk), we denote the difference sequence by Δx=(xk-xk-1). Let u=(uk)k=0∞ and v=(vk)k=0∞ be the sequences of real numbers such that uk≠0, vk≠0 for all k∈N. The difference sequence spaces of weighted means λ(u,v,Δ) are defined as λ(u,v,Δ)=x=(xk):W(x)∈λ, where λ= c,c0 and ℓ∞ and the matrix W=(wnk) is defined by wnk=un(vk-vk+1);(kn). In this paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on λ(u,v,Δ). Further, we characterize some classes of compact operators on these spaces by using the Hausdorff measure of noncompactness. © 2011 Elsevier Ltd. All rights reserved.