  Recently, Kim-Kim introduced the lambda-umbral calculus, in which the
lambda-Sheffer sequences occupy the central position. In this paper, we
introduce the fully degenerate Bell and the fully degenerate Dowling
polynomials, and investigate some properties and identities relating to those
polynomials with the help oflambda-umbral calculus. Here we note that the fully
degenerate Bell poynomials and the fully degenerate Dowling polynomials are
respectively degenerate versions of the Bell polynomials and the Dowling
polynomials,
  of which the latters are the natural extension of the Whitney numbers of the
second kind.
