The aim of this paper is to modify the generating functions for the Daehee numbers and polynomials and also for the Bernoulli numbers and polynomials of the second kind. By using these functions, we give relations between the λ-Bernoulli numbers and polynomials, Apostol type Daehee numbers and polynomials, the λ-Stirling numbers of the second kind and λ-Bernoulli numbers and polynomials of the second kind. Moreover, by using the p-adic Volkenborn integral, we derive combinatorial sums associated with the Apostol type Daehee numbers and polynomials.