Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 3 5 2016 1 7 New Extensions of Some Known Special Polynomials under the Theory of Multiple q-Calculus 128 139 EN Mehmet Acikgoz Serkan Araci Department of Economics, Faculty of Economics, Administrative and Social Science, Hasan Kalyoncu University, Gaziantep, Turkey U?ur Duran TJANT2015354 10.12691/tjant-3-5-4 2015 8 14 2015 10 20 2016 1 5 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.