  In a previous paper, Rahmani introduced a new family of p-Bernoulli numbers
and polynomials by means of the Gauss hypergeometric function. Motivated by
this paper and as a degenerate version of those numbers and polynomials, we
introduce the generalized degenerate Bernoulli numbers and polynomials again by
using the Gauss hypergeometric function. In addition, we introduce the
degenerate type Eulerian numbers as a degenerate version of Eulerian numbers.
For the generalized degenerate Bernoulli numbers, we express them in terms of
the degenerate Stirling numbers of the second kind, of the degenerate type
Eulerian numbers, of the degenerate $p$-Stirling numbers of the second kind and
of an integral on the unit interval. As to the generalized degenerate Bernoulli
polynomials, we represent them in terms of the degenerate Stirling polynomials
of the second kind.
