Complex Anal. Oper. Theory DOI 10.1007/s11785-012-0257-3 Complex Analysis and Operator Theory Approximation by Complex q -Szász–Kantorovich Operators in Compact Disks, q > 1 Sorin G. Gal · Nazim I. Mahmudov · Mustafa Kara Received: 28 December 2011 / Accepted: 9 July 2012 © Springer Basel AG 2012 Abstract In this paper, the exact order 1 q n , q > 1, in approximation and Voronovskaja-type results for the complex q -Szász–Kantorovich operators attached to analytic functions on compact disks are obtained. Keywords Complex q -Szász–Kantorovich operator with q > 1 · Compact disk · Upper estimates · Voronovskaja’s result · Exact order of approximation · Simultaneous approximation Mathematics Subject Classification (2000) 30E10 · 41A25 1 Introduction We will use the following notations (see, [5]). For each k ≥ 0, the q -integer [k ] q and the q -factorial [k ] q ! are defined by [k ] q :=  1-q k 1-q if q > 0, q  =1, k if q = 1  , Communicated by Wolfgang Sproessig. S. G. Gal · N. I. Mahmudov · M. Kara Department of Mathematics and Computer Science, University of Oradea, Str. Universitatii Nr. 1, 410087 Oradea, Romania e-mail: galso@uoradea.ro S. G. Gal · N. I. Mahmudov (B ) · M. Kara Department of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey e-mail: nazim.mahmudov@emu.edu.tr