  The aim of this paper is to introduce several degenerate hyperbolic functions
as degenerate versions of the hyperbolic functions, to evaluate Volkenborn and
the fermionic $p$-adic integrals of the degenerate hyperbolic cosine and the
degenerate hyperbolic sine functions and to derive from them some identities
involving the degenerate Bernoulli numbers, the degenerate Euler numbers and
the Cauchy numbers of the first kind.
