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Positivity of linear transformations of mean-starshaped sequences

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Abstract

In this paper, we give the necessary and sufficient conditions for a linear transformation of a mean-starshaped sequence to be positive. Using this result, we obtain the necessary and sufficient conditions for a lower triangular matrix to preserve the mean-starshape of a sequence and we discuss some special cases of linear transformations. Our next result deals with the convergence of a sequence of mean-starshaped sequences to any given mean-starshaped sequence and the positivity of a linear operator on the set of mean-starshaped sequences.

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Acknowledgments

We are greatful to the referee for suggesting to include the examples, improving the presentation of the paper immensely.

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  1. Penn State University-Shenango Campus, 147, Shenango Avenue, Sharon, PA, 16146, USA

    Chikkanna R. Selvaraj & Suguna Selvaraj

Authors
  1. Chikkanna R. Selvaraj
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  2. Suguna Selvaraj
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Correspondence to Chikkanna R. Selvaraj.

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Selvaraj, C.R., Selvaraj, S. Positivity of linear transformations of mean-starshaped sequences. Positivity 20, 805–822 (2016). https://doi.org/10.1007/s11117-015-0386-9

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  • DOI: https://doi.org/10.1007/s11117-015-0386-9

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