Science and Education Publishing Turkish Journal of Analysis and Number Theory ISSN Pending 1 1 2013 12 03 Some Relationships between the Generalized Apostol-Bernoulli and Apostol-Euler Polynomials 54 58 EN Burak Kurt Department of Mathematical Education, Faculty of Educations, Akdeniz University, TR-07058 Antalya, Turkey TJANT20131111 10.12691/tjant-1-1-11 2013 11 28 2013 11 30 2013 12 03 The main objective of this paper is to introduce and investigate two new classes of generalized Apostol-Bernoulli polynomials Bn[m-1,](x;c,;) and Apostol-Euler polynomials n[m-1,](x;c,;). In particular, we obtain addition formula for the new class of the generalized Apostol-Bernoulli polynomials. We also give some recurrence relations and Raabe relations for these polynomials.