\((\rho,q)\)-Volkenborn integration (Q331095)

\((\rho ,q)\)-calculus is a generalization of the \(q\)-calculus, in which the \((\rho ,q)\)-derivative, \((\rho ,q)\)-integral and various special functions are defined using a couple \((\rho ,q)\) of complex or \(p\)-adic numbers. In the paper under review, the authors define in this context a kind of Volkenborn's \(p\)-adic integral. This leads to a new generalization of Carlitz's \(q\)-Bernoulli numbers and polynomials including some identities for them.