Some array type polynomials associated with special numbers and polynomials

The main objective in this paper is first to establish new identities for the λ-Stirling type numbers of the second kind, the λ-array type polynomials, the Apostol-Bernoulli polynomials and the Apostol-Bernoulli numbers. We then construct a λ-delta operator and investigate various generating functions for the λ-Bell type numbers and for some new polynomials associated with the λ-array type polynomials. We also derive several other identities and relations for these polynomials and numbers.