Some identities on the generalized \(q\)-Bernoulli numbers and polynomials associated with \(q\)-Volkenborn integrals (Q607975)

In this paper, the authors give a systemic study of some families of multiple Carlitz's type \(q\)-Bernoulli numbers and polynomials by using the integral equations of \(p\)-adic \(q\)-integrals on \(\mathbb Z_p\). First, they derive some interesting equations of \(p\)-adic \(q\)-integrals on \(\mathbb Z_p\). From these equations, they give some interesting formulae for the higher-order Carlitz's type \(q\)-Bernoulli numbers and polynomials in \(\mathbb Z_p\).