New approach to the complete sum of products of the twisted (h, q)-Bernoulli numbers and polynomials

In this paper, by using q-Volkenborn integral[10], the first author[25] constructed new generating functions of the new twisted (h,q)-Bernoulli polynomials and numbers. We define higher-order twisted (h,q)-Bernoulli polynomials and numbers. Using these numbers and polynomials, we obtain new approach to the complete sums of products of twisted (h,q)-Bernoulli polynomials and numbers. p-adic q-Volkenborn integral is used to evaluate summations of the following form: B(m,w)((h,v)) (y(1) + y(2) +...+ y(v,q)) [GRAPHICS] where B(m,w)((h))(y(j),q) is the twisted (h,q)-Bernoulli polynomials. We also define new identities involving (h,q)-Bernoulli polynomials and numbers.