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On the Spectral Properties of the Weighted Mean Difference Operator over the Sequence Space

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  • P. Baliarsingh
  • S. Dutta

Abstract

In the present work the generalized weighted mean difference operator has been introduced by combining the generalized weighted mean and difference operator under certain special cases of sequences and . For any two sequences and of either constant or strictly decreasing real numbers satisfying certain conditions the difference operator is defined by with for all . Furthermore, we compute the spectrum and the fine spectrum of the operator over the sequence space . In fact, we determine the spectrum, the point spectrum, the residual spectrum, and the continuous spectrum of this operator on the sequence space .

Suggested Citation

  • P. Baliarsingh & S. Dutta, 2014. "On the Spectral Properties of the Weighted Mean Difference Operator over the Sequence Space," International Journal of Analysis, Hindawi, vol. 2014, pages 1-7, June.
    • Handle: RePEc:hin:ijanal:786437
    DOI: 10.1155/2014/786437
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