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)(y₁ + y₂ + ... + y_v, q) = ∑ _{l1,l2,...,lv ≥ 0 l1 + l2 + ... + lv = m} ( _l1,l2,...,lv^m) ∏_j=1^vB _lj,w^(h)(y_j, q), where B_m,w ^(h)(y_j, q) is the twisted (h, g)-Bernoulli polynomials. We also define new identities involving (h, q)-Bernoulli polnomials and numbers.