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Some Topological and Geometrical Properties of a New Difference Sequence Space

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  • Serkan Demiriz
  • Celal Çakan

Abstract

We introduce the new difference sequence space ð ‘Ž ð ‘Ÿ ð ‘ ( Δ ) . Further, it is proved that the space ð ‘Ž ð ‘Ÿ ð ‘ ( Δ ) is the BK-space including the space ð ‘ ð ‘£ ð ‘ , which is the space of sequences of pbounded variation. We also show that the spaces ð ‘Ž ð ‘Ÿ ð ‘ ( Δ ) , and â„“ ð ‘ are linearly isomorphic for 1 ≤ ð ‘ < ∞ . Furthermore, the basis and the ð ›¼ - , ð ›½ - and ð ›¾ - duals of the space ð ‘Ž ð ‘Ÿ ð ‘ ( Δ ) are determined. We devote the final section of the paper to examine some geometric properties of the space ð ‘Ž ð ‘Ÿ ð ‘ ( Δ ) .

Suggested Citation

  • Serkan Demiriz & Celal Çakan, 2011. "Some Topological and Geometrical Properties of a New Difference Sequence Space," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, March.
    • Handle: RePEc:hin:jnlaaa:213878
    DOI: 10.1155/2011/213878
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