Filomat, vol.34, no.2, pp.515-520, 2020 (SCI-Expanded)
© 2020, University of Nis. All rights reserved.Many mathematicians in ([1], [2], [5], [14], [20]) introduced and investigated the generalized q-Bernoulli numbers and polynomials and the generalized q-Euler numbers and polynomials and the generalized q-Gennochi numbers and polynomials. Mahmudov ([15], [16]) considered and investigated the q-Bernoulli polynomials B(α) n,q x, y in x, y of order α and the q-Euler polynomials E(α) n,q x, y in x, y of order α. In this work, we define generalized q-poly-Bernoulli polynomials B[k,α] n,q x, y in x, y of order α. We give new relations between the generalized q-poly-Bernoulli polynomials B[k,α] n,q x, y in x, y of order α and the generalized q-poly-Euler polynomials E[k,α] n,q x, y in x, y of order α and the q-Stirling numbers of the second kind S2,q (n,k).