Genuine q-Stancu-Bernstein–Durrmeyer Operators

In the present paper, we introduce genuine q-Stancu-Bernstein–Durrmeyer operators Znq,α(f;x). We calculate moments of these operators, Znq,α(tj;x) for j=0,1,2, which follows a symmetric pattern. also second order central moment Znq,α((t−x)2;x). give Korovkin-type theorem; estimate rate convergence continuous functions. Furthermore, prove local approximation theorem in terms modulus continuity; obtain direct Lipschitz-type maximal function β and global by using Ditzian-Totik order.