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.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science