FILOMAT, vol.30, no.4, pp.921-927, 2016 (SCI-Expanded)
Recently, many mathematicians (Karande and Thakare [6], Ozarslan [14], Ozden et. al. [15], El-Deouky et. al. [5]) have studied the unification of Bernoulli, Euler and Genocchi polynomials. They gave some recurrence relations and proved some theorems. Mahmudov [13] defined the new q-Apostol-Bernoulli and q-Apostol-Euler polynomials. Also he gave the analogous of the Srivastava-Pinter addition theorems. Kurt [8] gave the new identities and some relations for these polynomials. In this work, we give some recurrence relations for the unified q-Apostol-type polynomials related to multiple sums. By using generating functions we derive many new identities and recurrence relations associated with the q-Apostol-type Bernoulli, the q-Apostol-type Euler and the q-Apostol-type Genocchi polynomials and numbers and also the generalized Stirling type numbers of the second kind.