eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2016-01-07 3 5 128 139 10.12691/tjant-3-5-4 TJANT2015354 article Mehmet Acikgoz 1 Serkan Araci mtsrkn@hotmail.com 2 U?ur Duran 2 Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, Gaziantep, Turkey Department of Economics, Faculty of Economics, Administrative and Social Science, Hasan Kalyoncu University, Gaziantep, Turkey In the year 2014, the idea of multiple q-calculus was formulated and introduced in the book of Nalci and Pashaev [9] in which this idea is simple but elegant method in order to derive new generating functions of some special polynomials that are generalizations of known q-polynomials. In this paper, we will use Nalci and Pashaev's method in order to find a systematic study of new types of the Bernoulli polynomials, Euler polynomials and Genocchi polynomials. Also we will obtain recursive formulas for these polynomials. http://pubs.sciepub.com/tjant/3/5/4/tjant-3-5-4.pdf Quantum calculus Multiple quantum calculus q-Bernoulli polynomials q-Euler polynomials q-Genocchi polynomials Generating function