  We introduce new generalizations of the Bernoulli, Euler, and Genocchi
polynomials and numbers based on the Carlitz-Tsallis degenerate exponential
function and concepts of the Umbral Calculus associated with it. Also, we
present generalizations of some familiar identities and connection between
these kinds of Bernoulli, Euler, and Genocchi polynomials. Moreover, we
establish a new analogue of the Euler identity for the degenerate Bernoulli
numbers.
