Linear Transformations Preserving the Strong $q$-log-convexity of Polynomials
Keywords:
Log-concavity, Log-convexity, $q$-Log-convexity, Strong $q$-log-convexity
Abstract
In this paper, we give a sufficient condition for the linear transformation preserving the strong $q$-log-convexity. As applications, we get some linear transformations (for instance, Morgan-Voyce transformation, binomial transformation, Narayana transformations of two kinds) preserving the strong $q$-log-convexity. In addition, our results not only extend some known results, but also imply the strong $q$-log-convexities of some sequences of polynomials.