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On a Generalized Difference Operator and Its Fine Spectra

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Abstract

In the present article, we compute the spectra of the generalized difference operator \(B_\nu ^{(m)}\) over the sequence space \(c_0\). In fact, the difference operator \(B_\nu ^{(m)}\) usually generalizes several difference operators such as first-order difference operators (\(\Delta _{ab}, B(r,s),\Delta\) and \(\Delta _\nu\)), second-order difference operators (\(\Delta ^2, B(r,s,t)\) and \(\Delta _{uv}^2\)), third-order difference operator(B(r, s, t, u)), difference operators \((\Delta ^m\) and \(\Delta _\nu ^m)\) of order \(m\in {\mathbb{N}}\) and many others. Therefore, the results obtained are more general and interesting than those derived earlier.

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Authors and Affiliations

  1. Department of Mathematics, Gangadhar Meher University, Sambalpur, Odisha, 768004, India

    Pinakadhar Baliarsingh

  2. Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology, Bhubaneswar, 751024, India

    Pinakadhar Baliarsingh

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  1. Pinakadhar Baliarsingh
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Correspondence to Pinakadhar Baliarsingh.

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Baliarsingh, P. On a Generalized Difference Operator and Its Fine Spectra. Iran J Sci Technol Trans Sci 44, 779–786 (2020). https://doi.org/10.1007/s40995-020-00871-x

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  • DOI: https://doi.org/10.1007/s40995-020-00871-x

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