Approximation by $$q$$ q -Baskakov Durrmeyer type operators

Abstract

In the present article, we introduce the \(q\)-analogue of certain Baskakov Durrmeyer type operators. First, we establish the recurrence relation for 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 the modulus of continuity are studied. Lastly, in order to obtain better approximation we study a King type modification of the above operators.