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International Journal of Analysis
Volume 2014 (2014), Article ID 786437, 7 pages
Research Article

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

1Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar 751024, India
2Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar 751004, India

Received 21 December 2013; Accepted 30 April 2014; Published 16 June 2014

Academic Editor: Baruch Cahlon

Copyright © 2014 P. Baliarsingh and S. Dutta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 .