General Gamma type operators based on q-integers

In the present paper, we introduce the q-analogue of the general Gamma type operators. We establish the moments of the operators by using the q-derivatives and then prove the basic convergence theorem. Next, the Voronovskaja type theorem and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then, we obtain point-wise estimate using the Lipschitz type maximal function. Further, we study the A-statistical convergence of these operators. Lastly, we propose a king type modification of these operators to obtain better estimates. (C) 2014 Elsevier Inc. All rights reserved.