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Recently, the λ-analogues of r-Stirling numbers of the first kind were studied by Kim-Kim. The aim of this paper is to introduce the λ-analogues of r-Stirling numbers of the second kind and to investigate some properties, recurrence relations and certain identities on those numbers. We also introduce the λ-analogues of Whitney-type r-Stirling numbers of the second and derive similar results to the case of the λ-analogues of r-Stirling numbers of the second kind. In addition, we consider the λ-analogues of Dowling polynomials and deduce a Dobinski-like formula.
Kim et al. (Sun,) studied this question.