Abstract
This paper considers the generalized Stirling numbers of the first and second kinds. First, we show that the sequences of the above generalized Stirling numbers are both log-concave under some mild conditions. Then, we show that some polynomials related to the above generalized Stirling numbers are $q$-log-concave or $q$-log-convex under suitable conditions. We further discuss the log-convexity of some linear transformations related to generalized Stirling numbers of the first kind.
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