On q-analogue of a complex summation-integral type operators in compact disks

* Correspondence: [email protected] School of Applied Sciences, Netaji Subhas Institute of Technology, Sector 3 Dwarka, New Delhi110078, India Full list of author information is available at the end of the article Abstract Recently, Gupta and Wang introduced certain q-Durrmeyer type operators of real variable x Î [0, 1] and studied some approximation results in the case of real variables. Here we extend this study to the complex variable for analytic functions in compact disks. We establish the quantitative Voronovskaja type estimate. In this way, we put in evidence the over convergence phenomenon for these qDurrmeyer polynomials; namely, the extensions of approximation properties (with quantitative estimates) from the real interval [0,1] to compact disks in the complex plane. Some of these results for q = 1 were recently established in Gupta-Yadav. Mathematical subject classification (2000): 30E10; 41A25.