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