  The aim of this paper is to study the fully degenerate Bernoulli polynomials
and numbers, which are a degenerate version of Bernoulli polynomials and
numbers and arise naturally from the Volkenborn integral of the degenerate
exponential functions on Zp. We find some explicit expressions for the fully
degenerate Bernoulli polynomials and numbers in terms of the degenerate
Stirling numbers of the second kind, the degenerate r-Stirling numbers of the
second kind and of the degenerate Stirling polynomials.
  We also consider the degenerate poly-Bernoulli polynomials and derive
explicit representations for them in terms of the same degenerate Stirling
numbers and polynomials.
