On the analogs of Bernoulli and Euler numbers, related identities and zeta and L-functions

In this paper, by using q-deformed bosonic p-adic integral, we give λ-Bernoulli numbers and polynomials, we prove Witt's type formula of λ-Bernoulli polynomials and Gauss multiplicative formula for λ-Bernoulli polynomials. By using derivative operator to the generating functions of λ-Bernoulli polynomials and generalized λ-Bernoulli numbers, we give Hurwitz type λ-zeta functions and Dirichlet's type λ-L-functions; which are interpolated λ-Bernoulli polynomials and generalized λ-Bernoulli numbers, respectively. We give generating function of λ-Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and λ-Bernoulli polynomials and ordinary Bernoulli numbers of order r and λ-Bernoulli numbers, respectively. We also study on λ-Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define λ-partial zeta function and interpolation function.