# Complex line q-integrals and q-Green’s formula on the plane

 Received: 13.VII.2015, Accepted: 28.IV.2016 Abstract. In this study, we firstly present the line q-integral of a complex function f(z) on a piecewise smooth rectifiable curve $\gamma$ in complex plane. After that, on a square set, we define the multiple $q$-integral. At the end of this study, we prove the q-Green’s formula. Keywords: q-derivative, line q-integrals, q-multiple integral, q-Green’s formulas Mathematics Subject Classification (2010): 05A30, 30G25 Authors: İlker Gençtürk, Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey Kerim Koca, Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey Mustafa Aydin, Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey