... paper, Z, Q, Zp, Qp,andCpwill respectively denote the ring of rationalintegers, the field of rational numbers, the ring p-adic rational integers, the field of p-adicrational numbers, and ... to the second kind Stirling numbers and q-Bernstein polynomials. Finally, we derive the q-extensions of zeta functions from the Mellin transformation of this generating functionAdvances in Difference ... 8th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM’10), AIP, Rhodes, Greece, March 2010.2 M. Ac¸ıkg¨oz and Y. S¸ims¸ ek, A new generating function of q-Bernstein-type...