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